Tootfinder

Computing conservative probabilities of rare events with surrogates
Nicolas Bousquet
https://arxiv.org/abs/2403.17505 https://arxiv.o…

Computing conservative probabilities of rare events with surrogates
This article provides a critical review of the main methods used to produce conservative estimators of probabilities of rare events, or critical failures, for reliability and certification studies in the broadest sense. These probabilities must theoretically be calculated from simulations of (certified) numerical models, but which typically suffer from prohibitive computational costs. This occurs frequently, for instance, for complex and critical industrial systems. We focus therefore in adapti…

One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
Manuel D. De la Iglesia, Carlos F. Lardizabal
https://arxiv.org/abs/2402.15878

One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal (quantum) degrees of freedom. In this work we study continuous-time QMCs on the integer line, half-line and finite segments, so that we are able to obtain exact probability calculations in terms of the associated matrix-valued orthogonal polynomials and measures. Th…

On the upper and lower covariances under multiple probabilities
Xinpeng Li, Jingxu Niu, Ke Zhou
https://arxiv.org/abs/2402.17462 https://

On the upper and lower covariances under multiple probabilities
In this paper, we define the upper (resp. lower) covariance under multiple probabilities via a corresponding max-min-max (resp. min-max-min) optimization problem and the related properties of covariances are obtained. In particular, we propose a fast algorithm of calculation for upper and lower covariances under the finite number of probabilities. As an application, our algorithm can be used to solve a class of quadratic programming problem exactly, and we obtain a probabilistic representation …

Covariate-adjusted Group Sequential Comparisons of Survival Probabilities
Peter Zhang, Brent Logan, Michael Martens
https://arxiv.org/abs/2403.17117 https:…

Covariate-adjusted Group Sequential Comparisons of Survival Probabilities
In confirmatory clinical trials, survival outcomes are frequently studied and interim analyses for efficacy and/or futility are often desirable. Methods such as the log rank test and Cox regression model are commonly used to compare treatments in this setting. They rely on a proportional hazards (PH) assumption and are subject to type I error rate inflation and loss of power when PH are violated. Such violations may be expected a priori, particularly when the mechanisms of treatments differ suc…

One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
Manuel D. De la Iglesia, Carlos F. Lardizabal
https://arxiv.org/abs/2402.15878

One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal (quantum) degrees of freedom. In this work we study continuous-time QMCs on the integer line, half-line and finite segments, so that we are able to obtain exact probability calculations in terms of the associated matrix-valued orthogonal polynomials and measures. Th…

Two-layered logics for probabilities and belief functions over Belnap--Dunn logic
Marta Bilkova, Sabine Frittella, Daniil Kozhemiachenko, Ondrej Majer
https://arxiv.org/abs/2402.12953

Two-layered logics for probabilities and belief functions over Belnap--Dunn logic
This paper is an extended version of an earlier submission to WoLLIC 2023. We discuss two-layered logics formalising reasoning with probabilities and belief functions that combine the Lukasiewicz $[0,1]$-valued logic with Baaz $\triangle$ operator and the Belnap--Dunn logic. We consider two probabilistic logics that present two perspectives on the probabilities in the Belnap--Dunn logic: $\pm$-probabilities and $\mathbf{4}$-probabilities. In the first case, every event $ϕ$ has independent posi…

This https://arxiv.org/abs/2303.16971 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Sparse joint shift in multinomial classification
Sparse joint shift (SJS) was recently proposed as a tractable model for general dataset shift which may cause changes to the marginal distributions of features and labels as well as the posterior probabilities and the class-conditional feature distributions. Fitting SJS for a target dataset without label observations may produce valid predictions of labels and estimates of class prior probabilities. We present new results on the transmission of SJS from sets of features to larger sets of featur…

Contracts with Inspections
Tomer Ezra, Stefano Leonardi, Matteo Russo
https://arxiv.org/abs/2402.16553 https://arxiv.org/pdf/2402.165…

Contracts with Inspections
In the classical principal-agent hidden-action model, a principal delegates the execution of a costly task to an agent for which he can choose among actions with different costs and different success probabilities to accomplish the task. To incentivize the agent to exert effort, the principal can commit to a contract, which is the amount of payment based on the task's success. A crucial assumption of this model is that the principal can only base the payment on the outcome but not on the agent'…

This https://arxiv.org/abs/2402.13376 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csFL_…

Probabilistic automatic complexity of finite strings
We introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least number of states of a PFA for which $x$ is the most likely string of its length to be accepted. The variant $A_{P,δ}(x)$ adds a real-valued parameter $δ$ specifying a lower bound on the gap in acceptance probabilities between $x$ and other strings. We relat…

$(\omega_1, \omega_2)$-Temporal random hyperbolic graphs
Sofoclis Zambirinis, Fragkiskos Papadopoulos
https://arxiv.org/abs/2403.17440 https://

$(ω_1, ω_2)$-Temporal random hyperbolic graphs
We extend a recent model of temporal random hyperbolic graphs by allowing connections and disconnections to persist across network snapshots with different probabilities, $ω_1$ and $ω_2$. This extension, while conceptually simple, poses analytical challenges involving the Appell $F_1$ series. Despite these challenges, we are able to analyze key properties of the model, which include the distributions of contact and intercontact durations, as well as the expected time-aggregated degree. The in…

Unraveling the collinearity in short-range order parameters for lattice configurations arising from topological constraints
Abhijit Chatterjee
https://arxiv.org/abs/2403.18380

Unraveling the collinearity in short-range order parameters for lattice configurations arising from topological constraints
In multicomponent lattice problems, e.g., in alloys, and at crystalline surfaces and interfaces, atomic arrangements exhibit spatial correlations that dictate the kinetic and thermodynamic phase behavior. These correlations emerge from interparticle interactions and are frequently reported in terms of the short-range order (SRO) parameter. Expressed usually in terms of pair distributions and other cluster probabilities, the SRO parameter gives the likelihood of finding atoms/molecules of a part…

This https://arxiv.org/abs/2308.12194 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csHC_…

Inferring Human Intentions from Predicted Action Probabilities
Predicting the next action that a human is most likely to perform is key to human-AI collaboration and has consequently attracted increasing research interests in recent years. An important factor for next action prediction are human intentions: If the AI agent knows the intention it can predict future actions and plan collaboration more effectively. Existing Bayesian methods for this task struggle with complex visual input while deep neural network (DNN) based methods do not provide uncertaint…

"My Answer is C": First-Token Probabilities Do Not Match Text Answers in Instruction-Tuned Language Models
Xinpeng Wang, Bolei Ma, Chengzhi Hu, Leon Weber-Genzel, Paul R\"ottger, Frauke Kreuter, Dirk Hovy, Barbara Plank
https://arxiv.org/abs/2402.14499

"My Answer is C": First-Token Probabilities Do Not Match Text Answers in Instruction-Tuned Language Models
The open-ended nature of language generation makes the evaluation of autoregressive large language models (LLMs) challenging. One common evaluation approach uses multiple-choice questions (MCQ) to limit the response space. The model is then evaluated by ranking the candidate answers by the log probability of the first token prediction. However, first-tokens may not consistently reflect the final response output, due to model's diverse response styles such as starting with "Sure" or refusing to …

Comparing basic statistical concepts with diagnostic probabilities based on directly observed proportions to help understand the replication crisis
Huw Llewelyn
https://arxiv.org/abs/2403.16906

Comparing basic statistical concepts with diagnostic probabilities based on directly observed proportions to help understand the replication crisis
Instead of regarding an observed proportion as a sample from a population with an unknown parameter, diagnosticians intuitively use the observed proportion as a direct estimate of the posterior probability of a diagnosis. Therefore, a diagnostician might also regard a continuous Gaussian probability distribution of an outcome conditional on a study selection criterion to represents posterior probabilities. Fitting a distribution to its mean and standard deviation (SD) can be regarded as pooling…

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression
Agniva Chowdhury, Pradeep Ramuhalli
https://arxiv.org/abs/2402.16326 https://

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural con…

Asymptotics of the Smallest Eigenvalue Distributions of Freud Unitary Ensembles
Chao Min, Liwei Wang
https://arxiv.org/abs/2402.15190 https://

Asymptotics of the Smallest Eigenvalue Distributions of Freud Unitary Ensembles
We consider the smallest eigenvalue distributions of some Freud unitary ensembles, that is, the probabilities that all the eigenvalues of the Hermitian matrices from the ensembles lie in the interval $(t,\infty)$. This problem is related to the Hankel determinants generated by the Freud weights with a jump discontinuity. By using Chen and Ismail's ladder operator approach, we obtain the discrete systems for the recurrence coefficients of the corresponding orthogonal polynomials. This enables us…

This https://arxiv.org/abs/2309.06900 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Fast Exact Algorithm for Neutrino Oscillation in Constant Matter Density
A recently published method for solving the neutrino evolution equation with constant matter density is further refined and used to lay out an exact algorithm for computing oscillation probabilities, which is moderately faster than previous methods when looping through neutrinos of different energies. In particular, the three examples of $\overset{\scriptscriptstyle{(-)}}ν_e$ survival, $\overset{\scriptscriptstyle{(-)}}ν_μ$ survival and $\overset{\scriptscriptstyle{(-)}}ν_e$ appearance prob…

Predictable Interval MDPs through Entropy Regularization
Menno van Zutphen, Giannis Delimpaltadakis, Maurice Heemels, Duarte Antunes
https://arxiv.org/abs/2403.16711

Predictable Interval MDPs through Entropy Regularization
Regularization of control policies using entropy can be instrumental in adjusting predictability of real-world systems. Applications benefiting from such approaches range from, e.g., cybersecurity, which aims at maximal unpredictability, to human-robot interaction, where predictable behavior is highly desirable. In this paper, we consider entropy regularization for interval Markov decision processes (IMDPs). IMDPs are uncertain MDPs, where transition probabilities are only known to belong to in…

Evaluating the Security of Merkle Trees in the Internet of Things: An Analysis of Data Falsification Probabilities
Oleksandr Kuznetsov, Alex Rusnak, Anton Yezhov, Kateryna Kuznetsova, Dzianis Kanonik, Oleksandr Domin
https://arxiv.org/abs/2404.12093

Evaluating the Security of Merkle Trees in the Internet of Things: An Analysis of Data Falsification Probabilities
Addressing the critical challenge of ensuring data integrity in decentralized systems, this paper delves into the underexplored area of data falsification probabilities within Merkle Trees, which are pivotal in blockchain and Internet of Things (IoT) technologies. Despite their widespread use, a comprehensive understanding of the probabilistic aspects of data security in these structures remains a gap in current research. Our study aims to bridge this gap by developing a theoretical framework t…

Sizing the bets in a focused portfolio
Vuko Vukcevic, Robert Keser
https://arxiv.org/abs/2402.15588 https://arxiv.org/pdf/2402.15588<…

Sizing the bets in a focused portfolio
The paper provides a mathematical model and a tool for the focused investing strategy as advocated by Buffett, Munger, and others from this investment community. The approach presented here assumes that the investor's role is to think about probabilities of different outcomes for a set of businesses. Based on these assumptions, the tool calculates the optimal allocation of capital for each of the investment candidates. The model is based on a generalized Kelly Criterion with options to provide …

This https://arxiv.org/abs/2310.06135 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Probabilistic and Maximum Entropy Modeling of Chemical Reaction Systems: Characteristics and Comparisons to Mass Action Kinetic Models
We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between the entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics an…

This https://arxiv.org/abs/2306.10594 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A nonparametric test for elliptical distribution based on kernel embedding of probabilities
Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data dependence structure. Before applying such methods, we need to decide whether the data are elliptically distributed. Currently existing tests either focus exclusively on spherical distributions, or rely on bootstrap to determine the null distribution, or require s…

A Blaschke-Petkantschin formula for linear and affine subspaces with application to intersection probabilities
Emil Dare, Markus Kiderlen, Christoph Thaele
https://arxiv.org/abs/2404.14253

A Blaschke-Petkantschin formula for linear and affine subspaces with application to intersection probabilities
Consider a uniformly distributed random linear subspace $L$ and a stochastically independent random affine subspace $E$ in $\mathbb{R}^n$, both of fixed dimension. For a natural class of distributions for $E$ we show that the intersection $L\cap E$ admits a density with respect to the invariant measure. This density depends only on the distance $d(o,E \cap L)$ of $L\cap E$ to the origin and is derived explicitly. It can be written as the product of a power of $d(o,E \cap L)$ and a part involvin…

This https://arxiv.org/abs/2212.06072 has been replaced.
link: https://scholar.google.com/scholar?q=a

Tunneling effect of fermions in silicene through potential barrier
The influence of a rectangular potential barrier on the quantum transport of fermions in silicene is explored. Specifically, analytical solutions are presented to derive transmission and reflection probabilities together with conductance. It is shown that the transmission is highly sensitive to both the barrier height and incident energy. As a result, the occurrence of Klein and resonant tunnelings is observed, with a significant dependence on the barrier width. Notably, it is found that perfec…

Incorporating Expert Rules into Neural Networks in the Framework of Concept-Based Learning
Andrei V. Konstantinov, Lev V. Utkin
https://arxiv.org/abs/2402.14726

Incorporating Expert Rules into Neural Networks in the Framework of Concept-Based Learning
A problem of incorporating the expert rules into machine learning models for extending the concept-based learning is formulated in the paper. It is proposed how to combine logical rules and neural networks predicting the concept probabilities. The first idea behind the combination is to form constraints for a joint probability distribution over all combinations of concept values to satisfy the expert rules. The second idea is to represent a feasible set of probability distributions in the form …

Markov chain models for inspecting response dynamics in psychological testing
Andrea Bosco
https://arxiv.org/abs/2403.17982 https://a…

Markov chain models for inspecting response dynamics in psychological testing
The importance of considering contextual probabilities in shaping response patterns within psychological testing is underscored, despite the ubiquitous nature of order effects discussed extensively in methodological literature. Drawing from concepts such as path-dependency, first-order autocorrelation, state-dependency, and hysteresis, the present study is an attempt to address how earlier responses serve as an anchor for subsequent answers in tests, surveys, and questionnaires. Introducing the…

This https://arxiv.org/abs/2309.07289 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csHC_…

User Training with Error Augmentation for Electromyogram-based Gesture Classification
We designed and tested a system for real-time control of a user interface by extracting surface electromyographic (sEMG) activity from eight electrodes in a wrist-band configuration. sEMG data were streamed into a machine-learning algorithm that classified hand gestures in real-time. After an initial model calibration, participants were presented with one of three types of feedback during a human-learning stage: veridical feedback, in which predicted probabilities from the gesture classificatio…

This https://arxiv.org/abs/2302.13675 has been replaced.
link: https://scholar.google.com/scholar?q=a

Positivity-hardness results on Markov decision processes
This paper investigates a series of optimization problems for one-counter Markov decision processes (MDPs) and integer-weighted MDPs with finite state space. Specifically, it considers problems addressing termination probabilities and expected termination times for one-counter MDPs, as well as satisfaction probabilities of energy objectives, conditional and partial expectations, satisfaction probabilities of constraints on the total accumulated weight, the computation of quantiles for the accum…

Asymptotics of the Smallest Eigenvalue Distributions of Freud Unitary Ensembles
Chao Min, Liwei Wang
https://arxiv.org/abs/2402.15190 https://

Asymptotics of the Smallest Eigenvalue Distributions of Freud Unitary Ensembles
We consider the smallest eigenvalue distributions of some Freud unitary ensembles, that is, the probabilities that all the eigenvalues of the Hermitian matrices from the ensembles lie in the interval $(t,\infty)$. This problem is related to the Hankel determinants generated by the Freud weights with a jump discontinuity. By using Chen and Ismail's ladder operator approach, we obtain the discrete systems for the recurrence coefficients of the corresponding orthogonal polynomials. This enables us…

Fill Probabilities in a Limit Order Book with State-Dependent Stochastic Order Flows
Felix Lokin, Fenghui Yu
https://arxiv.org/abs/2403.02572 https://

Fill Probabilities in a Limit Order Book with State-Dependent Stochastic Order Flows
This paper focuses on computing the fill probabilities for limit orders positioned at various price levels within the limit order book, which play a crucial role in optimizing executions. We adopt a generic stochastic model to capture the dynamics of the order book as a series of queueing systems. This generic model is state-dependent and also incorporates stylized factors. We subsequently derive semi-analytical expressions to compute the relevant probabilities within the context of state-depen…

This https://arxiv.org/abs/2108.09989 has been replaced.
link: https://scholar.google.com/scholar?q=a

Decoding Error Probability of the Random Matrix Ensemble over the Erasure Channel
Using tools developed in a recent work by Shen and the second author, in this paper we carry out an in-depth study on the average decoding error probability of the random matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random matrix ensemble under these three decoding principles and compute the error exponents. More…

Detecting stellar flares in photometric data using hidden Markov models
J. Arturo Esquivel, Yunyi Shen, Vianey Leos-Barajas, Gwendolyn Eadie, Joshua Speagle, Radu V Craiu, Amber Medina, James Davenport
https://arxiv.org/abs/2404.13145

Detecting stellar flares in photometric data using hidden Markov models
We present a hidden Markov model (HMM) for discovering stellar flares in light curve data of stars. HMMs provide a framework to model time series data that are not stationary; they allow for systems to be in different states at different times and consider the probabilities that describe the switching dynamics between states. In the context of stellar flares discovery, we exploit the HMM framework by allowing the light curve of a star to be in one of three states at any given time step: Quiet, …

Mixed strategy approach destabilizes cooperation in finite populations with clustering coefficient
Zehua Si, Zhixue He, Chen Shen, Jun Tanimoto
https://arxiv.org/abs/2402.15091

Mixed strategy approach destabilizes cooperation in finite populations with clustering coefficient
Evolutionary game theory, encompassing discrete, continuous, and mixed strategies, is pivotal for understanding cooperation dynamics. Discrete strategies involve deterministic actions with a fixed probability of one, whereas continuous strategies employ intermediate probabilities to convey the extent of cooperation and emphasize expected payoffs. Mixed strategies, though akin to continuous ones, calculate immediate payoffs based on the action chosen at a given moment within intermediate probabi…

This https://arxiv.org/abs/2310.12716 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

A contextuality witness inspired by optimal state discrimination
Many protocols and tasks in quantum information science rely inherently on the fundamental notion of contextuality to provide advantages over their classical counterparts, and contextuality represents one of the main differences between quantum and classical physics. In this work we present a witness for preparation contextuality inspired by optimal two-state discrimination. The main idea is based on finding the accessible averaged success and error probabilities in both classical and quantum m…

Level-2 IFS Thermodynamic Formalism: Gibbs probabilities in the space of probabilities and the push-forward map
A. O. Lopes, E. R. Oliveira
https://arxiv.org/abs/2403.19566

Level-2 IFS Thermodynamic Formalism: Gibbs probabilities in the space of probabilities and the push-forward map
We will denote by $\mathcal{M}$ the space of Borel probabilities on the symbolic space $Ω=\{1,2...,m\}^\mathbb{N}$. $\mathcal{M}$ is equipped Monge-Kantorovich metric. We consider here the push-forward map $\mathfrak{T}:\mathcal{M} \to \mathcal{M}$ as a dynamical system. The space of Borel probabilities on $\mathcal{M}$ is denoted by $\mathfrak{M}$. Given a continuous function $A: \mathcal{M}\to \mathbb{R}$, an {\it a priori} probability $Π_0$ on $\mathcal{M}$, and a certain convolution opera…

This https://arxiv.org/abs/2402.13391 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

De-Biasing the Bias: Methods for Improving Disparity Assessments with Noisy Group Measurements
Health care decisions are increasingly informed by clinical decision support algorithms, but these algorithms may perpetuate or increase racial and ethnic disparities in access to and quality of health care. Further complicating the problem, clinical data often have missing or poor quality racial and ethnic information, which can lead to misleading assessments of algorithmic bias. We present novel statistical methods that allow for the use of probabilities of racial/ethnic group membership in a…

A Tight $O(4^k/p_c)$ Runtime Bound for a ($\mu$ 1) GA on Jump$_k$ for Realistic Crossover Probabilities
Andre Opris, Johannes Lengler, Dirk Sudholt
https://arxiv.org/abs/2404.07061

A Tight $O(4^k/p_c)$ Runtime Bound for a ($μ$+1) GA on Jump$_k$ for Realistic Crossover Probabilities
The Jump$_k$ benchmark was the first problem for which crossover was proven to give a speedup over mutation-only evolutionary algorithms. Jansen and Wegener (2002) proved an upper bound of $O({\rm poly}(n) + 4^k/p_c)$ for the ($μ$+1)~Genetic Algorithm ($(μ+1)$ GA), but only for unrealistically small crossover probabilities $p_c$. To this date, it remains an open problem to prove similar upper bounds for realistic~$p_c$; the best known runtime bound for $p_c = Ω(1)$ is $O((n/χ)^{k-1})$, $χ$…

Maxentropy completion and properties of some partially defined Stationary Markov chains
Pierre ColletCPHT, CNRS, Ecole Polytechnique, IP Paris, Servet Mart\'inezDepartamento de Ingenier\'ia Matem\'atica,Centro de Modelamiento Matem\'atico Universidad de Chile
https://arxiv.org/abs/2402.14019

Maxentropy completion and properties of some partially defined Stationary Markov chains
We consider a stationary Markovian evolution with values on a disjointly partitioned set space $I\sqcup {\cal E}$. The evolution is visible (in the sense of knowing the transition probabilities) on the states in $I$ but not for the states in ${\cal E}$. One only knows some partial information on the transition probabilities on ${\cal E}$, the input and output transition probabilities and some constraints of the transition probabilities on ${\cal E}$. Under some conditions we supply the transiti…

On Modeling Multi-Criteria Decision Making with Uncertain Information using Probabilistic Rules
Shengxin Hong, Xiuyi Fan
https://arxiv.org/abs/2404.13419 h…

On Modeling Multi-Criteria Decision Making with Uncertain Information using Probabilistic Rules
Decision-making processes often involve dealing with uncertainty, which is traditionally addressed through probabilistic models. However, in practical scenarios, assessing probabilities reliably can be challenging, compounded by diverse perceptions of probabilistic information among decision makers. To address this variability and accommodate diverse preferences regarding uncertainty, we introduce the Probabilistic Abstract Decision Framework (PADF). PADF offers a structured approach for reason…

What Are the Odds? Improving the foundations of Statistical Model Checking
Tobias Meggendorfer, Maximilian Weininger, Patrick Wienh\"oft
https://arxiv.org/abs/2404.05424

What Are the Odds? Improving the foundations of Statistical Model Checking
Markov decision processes (MDPs) are a fundamental model for decision making under uncertainty. They exhibit non-deterministic choice as well as probabilistic uncertainty. Traditionally, verification algorithms assume exact knowledge of the probabilities that govern the behaviour of an MDP. As this assumption is often unrealistic in practice, statistical model checking (SMC) was developed in the past two decades. It allows to analyse MDPs with unknown transition probabilities and provide probab…

This https://arxiv.org/abs/2309.06900 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Fast Exact Algorithm for Neutrino Oscillation in Constant Matter Density
A recently published method for solving the neutrino evolution equation with constant matter density is further refined and used to lay out an exact algorithm for computing oscillation probabilities, which is moderately faster than previous methods when looping through neutrinos of different energies. In particular, the three examples of $\overset{\scriptscriptstyle{(-)}}ν_e$ survival, $\overset{\scriptscriptstyle{(-)}}ν_μ$ survival and $\overset{\scriptscriptstyle{(-)}}ν_e$ appearance prob…

The distribution of $a$-numbers of hyperelliptic curves in characteristic three
Derek Garton, Jeffrey Lin Thunder, Colin Weir
https://arxiv.org/abs/2403.00120

The distribution of $a$-numbers of hyperelliptic curves in characteristic three
In this paper we present a new approach to counting the proportion of hyperelliptic curves of genus $g$ defined over a finite field $\mathbb{F}_q$ with a given $a$-number. In characteristic three this method gives exact probabilities for curves of the form $Y^2=f(X)$ with $f(X)\in\mathbb{F}_q[X]$ monic and cubefree, probabilities that match the data presented by Cais et al. in previous work. These results are sufficient to derive precise estimates (in terms of $q$) for these probabilities when …

A Markov approach to credit rating migration conditional on economic states
Michael Kalkbrener, Natalie Packham
https://arxiv.org/abs/2403.14868 https://…

A Markov approach to credit rating migration conditional on economic states
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain. While the rating process itself possesses the Markov property only under restrictive conditions, methods from Markov theory can be used to derive the rating process' asymptotic behaviour. We use the mathematical framework to formalise and analyse different ratin…

How curved is a random complex curve?
Michele AnconaLJAD, Damien GayetIF
https://arxiv.org/abs/2402.11972 https://arxiv.org/pdf/2402.…

How curved is a random complex curve?
In this paper, we study the curvature properties of random complex plane curves. We bound from below the probability that a uniform proportion of the area of a random complex degree $d$ plane curve has a curvature smaller than $-d/8$. Our lower bound is uniform, in the sense that it does not depend on $d$. We also provide uniform upper bounds for similar probabilities. These results extend to random complex curves of projective surfaces equipped with an ample line bundle. This paper can be view…

Space-Efficient Indexes for Uncertain Strings
Esteban Gabory, Chang Liu, Grigorios Loukides, Solon P. Pissis, Wiktor Zuba
https://arxiv.org/abs/2403.14256 …

Space-Efficient Indexes for Uncertain Strings
Strings in the real world are often encoded with some level of uncertainty. In the character-level uncertainty model, an uncertain string $X$ of length $n$ on an alphabet $Σ$ is a sequence of $n$ probability distributions over $Σ$. Given an uncertain string $X$ and a weight threshold $\frac{1}{z}\in(0,1]$, we say that pattern $P$ occurs in $X$ at position $i$, if the product of probabilities of the letters of $P$ at positions $i,\ldots,i+|P|-1$ is at least $\frac{1}{z}$. While index…

SED Analysis of the Old Open Cluster NGC 188
Deniz Cennet Dursun, Seval Ta\c{s}demir, Seliz Ko\c{c}, Srishti \.Iyer
https://arxiv.org/abs/2404.13115 https:…

SED Analysis of the Old Open Cluster NGC 188
In this study, we investigate the fundamental astrophysical parameters of the old open cluster NGC 188 through two complementary methods: isochron-fitting and spectral energy distribution (SED) analysis. Using photometric, astrometric, and spectroscopic data from the Gaia Data Release 3, we identify 868 most likely member stars with membership probabilities $P \geq 0.5$. The mean proper-motion components and trigonometric parallaxes of the cluster are derived as ($μ_α\cos δ$, $μ_δ$) = (-$2…

This https://arxiv.org/abs/2401.10638 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Accurately Computing Expected Visiting Times and Stationary Distributions in Markov Chains
We study the accurate and efficient computation of the expected number of times each state is visited in discrete- and continuous-time Markov chains. To obtain sound accuracy guarantees efficiently, we lift interval iteration and topological approaches known from the computation of reachability probabilities and expected rewards. We further study applications of expected visiting times, including the sound computation of the stationary distribution and expected rewards conditioned on reaching m…

This https://arxiv.org/abs/2105.12801 has been replaced.
link: https://scholar.google.com/scholar?q=a

Dialectica Petri Nets
The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets generalising the original application to suggest that Petri nets with different kinds of transitions can be modelled in the same categorical framework. Transitions representing truth-values, probabilities, rates or multiplicities, evaluated in different algebraic …

This https://arxiv.org/abs/2404.07520 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

PromptSync: Bridging Domain Gaps in Vision-Language Models through Class-Aware Prototype Alignment and Discrimination
The potential for zero-shot generalization in vision-language (V-L) models such as CLIP has spurred their widespread adoption in addressing numerous downstream tasks. Previous methods have employed test-time prompt tuning to adapt the model to unseen domains, but they overlooked the issue of imbalanced class distributions. In this study, we explicitly address this problem by employing class-aware prototype alignment weighted by mean class probabilities obtained for the test sample and filtered …

Betting on what is neither verifiable nor falsifiable
Abhimanyu Pallavi Sudhir, Long Tran-Thanh
https://arxiv.org/abs/2402.14021 https://

Betting on what is neither verifiable nor falsifiable
Prediction markets are useful for estimating probabilities of claims whose truth will be revealed at some fixed time -- this includes questions about the values of real-world events (i.e. statistical uncertainty), and questions about the values of primitive recursive functions (i.e. logical or algorithmic uncertainty). However, they cannot be directly applied to questions without a fixed resolution criterion, and real-world applications of prediction markets to such questions often amount to pr…

Martin boundary of a space-time Brownian motion with drift killed at the boundary of a moving cone
Sandro Franceschi
https://arxiv.org/abs/2404.16679 https…

Martin boundary of a space-time Brownian motion with drift killed at the boundary of a moving cone
We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0

Combinatorial correlation functions in three-dimensional eight-vertex models
Igor G. Korepanov
https://arxiv.org/abs/2402.12012 https://

Combinatorial correlation functions in three-dimensional eight-vertex models
A new version of the self-similarity spin transform on three-dimensional cubic lattices is proposed that makes possible calculation of nontrivial spin correlations in a "combinatorial" model, in which all permitted spin configurations have equal probabilities.

This https://arxiv.org/abs/2304.08061 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Provable local learning rule by expert aggregation for a Hawkes network
We propose a simple network of Hawkes processes as a cognitive model capable of learning to classify objects. Our learning algorithm, named HAN for Hawkes Aggregation of Neurons, is based on a local synaptic learning rule based on spiking probabilities at each output node. We were able to use local regret bounds to prove mathematically that the network is able to learn on average and even asymptotically under more restrictive assumptions.

This https://arxiv.org/abs/2308.15582 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Investigating Mass Segregation of the Binary Stars in the Open Cluster NGC 6819
We search for mass segregation in the intermediate-aged open cluster NGC 6819 within a carefully identified sample of probable cluster members. Using photometry from the Gaia, 2MASS, and Pan-STARRS surveys as inputs for a Bayesian statistics software suite, BASE-9, we identify a rich population of (photometric) binaries and derive posterior distributions for the cluster age, distance, metallicity and reddening as well as star-by-star photometric membership probabilities, masses and mass ratios …

Level-2 IFS Thermodynamic Formalism: Gibbs probabilities in the space of probabilities and the push-forward map
A. O. Lopes, E. R. Oliveira
https://arxiv.org/abs/2403.19566

Level-2 IFS Thermodynamic Formalism: Gibbs probabilities in the space of probabilities and the push-forward map
We will denote by $\mathcal{M}$ the space of Borel probabilities on the symbolic space $Ω=\{1,2...,m\}^\mathbb{N}$. $\mathcal{M}$ is equipped Monge-Kantorovich metric. We consider here the push-forward map $\mathfrak{T}:\mathcal{M} \to \mathcal{M}$ as a dynamical system. The space of Borel probabilities on $\mathcal{M}$ is denoted by $\mathfrak{M}$. Given a continuous function $A: \mathcal{M}\to \mathbb{R}$, an {\it a priori} probability $Π_0$ on $\mathcal{M}$, and a certain convolution opera…

The Logarithmic Random Bidding for the Parallel Roulette Wheel Selection with Precise Probabilities
Koji Nakano
https://arxiv.org/abs/2402.18110 https://…

The Logarithmic Random Bidding for the Parallel Roulette Wheel Selection with Precise Probabilities
The roulette wheel selection is a critical process in heuristic algorithms, enabling the probabilistic choice of items based on assigned fitness values. It selects an item with a probability proportional to its fitness value. This technique is commonly employed in ant-colony algorithms to randomly determine the next city to visit when solving the traveling salesman problem. Our study focuses on parallel algorithms designed to select one of multiple processors, each associated with fitness value…

Probabilistic automatic complexity of finite strings
Kenneth Gill
https://arxiv.org/abs/2402.13376 https://arxiv.org/pdf/2402.13376…

Probabilistic automatic complexity of finite strings
We introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least number of states of a PFA for which $x$ is the most likely string of its length to be accepted. The variant $A_{P,δ}(x)$ adds a real-valued parameter $δ$ specifying a lower bound on the gap in acceptance probabilities between $x$ and other strings. We relat…

This https://arxiv.org/abs/2403.03052 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Simulation of Chemical Reactions on a Quantum Computer
Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum algorithm for the calculat…

This https://arxiv.org/abs/2305.18582 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Information Association for Language Model Updating by Mitigating LM-Logical Discrepancy
Large Language Models~(LLMs) struggle with providing current information due to the outdated pre-training data. Existing methods for updating LLMs, such as knowledge editing and continual fine-tuning, have significant drawbacks in generalizability of new information and the requirements on structured updating corpus. We identify the core challenge behind these drawbacks: the LM-logical discrepancy featuring the difference between language modeling probabilities and logical probabilities. To eva…

A Method For Bounding Tail Probabilities
Nikola Zlatanov
https://arxiv.org/abs/2402.13662 https://arxiv.org/pdf/2402.13662

A Method For Bounding Tail Probabilities
We present a method for upper and lower bounding the right and the left tail probabilities of continuous random variables (RVs). For the right tail probability of RV $X$ with probability density function $f_X(x)$, this method requires first setting a continuous, positive, and strictly decreasing function $g_X(x)$ such that $-f_X(x)/g'_X(x)$ is a decreasing and increasing function, $\forall x>x_0$, which results in upper and lower bounds, respectively, given in the form $-f_X(x) g_X(x)/g'_X(x)$,…

This https://arxiv.org/abs/2303.04097 has been replaced.
link: https://scholar.google.com/scholar?q=a

On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation
Properties of the additive differential probability $\mathrm{adp}^{\mathrm{XR}}$ of the composition of bitwise XOR and a bit rotation are investigated, where the differences are expressed using addition modulo $2^n$. This composition is widely used in ARX constructions consisting of additions modulo $2^n$, bit rotations and bitwise XORs. Differential cryptanalysis of such primitives may involve maximums of $\mathrm{adp}^{\mathrm{XR}}$, where some of its input or output differences are fixed. Al…

Space-Efficient Indexes for Uncertain Strings
Esteban Gabory, Chang Liu, Grigorios Loukides, Solon P. Pissis, Wiktor Zuba
https://arxiv.org/abs/2403.14256 …

Space-Efficient Indexes for Uncertain Strings
Strings in the real world are often encoded with some level of uncertainty. In the character-level uncertainty model, an uncertain string $X$ of length $n$ on an alphabet $Σ$ is a sequence of $n$ probability distributions over $Σ$. Given an uncertain string $X$ and a weight threshold $\frac{1}{z}\in(0,1]$, we say that pattern $P$ occurs in $X$ at position $i$, if the product of probabilities of the letters of $P$ at positions $i,\ldots,i+|P|-1$ is at least $\frac{1}{z}$. While index…

This https://arxiv.org/abs/2210.09095 has been replaced.
link: https://scholar.google.com/scholar?q=a

Qualitative reasoning in a two-layered framework
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In the first part, we formalise reasoning with the qualitative counterparts of capacities, belief functions, and probabilities, within the framework of two-layered logics. Namely, we provide two-layered logics built over the classical propositional logic using a u…

This https://arxiv.org/abs/2209.05812 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Non-Parametric Bootstrap for Spectral Clustering
Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which can utilize the expectation-maximization (EM) algorithm. However, the EM algorithm falls victim to a number of issues, including convergence to sub-optimal solutions. We address this issue by developing two novel algorithms that incorporate the spectral decompo…

This https://arxiv.org/abs/2310.03643 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Invariant measures for place dependent idempotent iterated function systems
We study the set of invariant idempotent probabilities for place dependent idempotent iterated function systems defined in compact metric spaces. Using well-known ideas from dynamical systems, such as the Mañé potential and the Aubry set, we provide a complete characterization of the densities of such idempotent probabilities. As an application, we provide an alternative formula for the attractor of a class of fuzzy iterated function systems.

This https://arxiv.org/abs/2402.05414 has been replaced.
link: https://scholar.google.com/scholar?q=a

Splitting probabilities as optimal controllers of rare reactive events
The committor constitutes the primary quantity of interest within chemical kinetics as it is understood to encode the ideal reaction coordinate for a rare reactive event. We show the generative utility of the committor, in that it can be used explicitly to produce a reactive trajectory ensemble that exhibits numerically exact statistics as that of the original transition path ensemble. This is done by relating a time-dependent analogue of the committor that solves a generalized bridge problem, …

This https://arxiv.org/abs/2308.14339 has been replaced.
link: https://scholar.google.com/scholar?q=a

Entropy-Based Strategies for Multi-Bracket Pools
Much work in the parimutuel betting literature has discussed estimating event outcome probabilities or developing optimal wagering strategies, particularly for horse race betting. Some betting pools, however, involve betting not just on a single event, but on a tuple of events. For example, pick six betting in horse racing, March Madness bracket challenges, and predicting a randomly drawn bitstring each involve making a series of individual forecasts. Although traditional optimal wagering strat…

This https://arxiv.org/abs/2305.18582 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Information Association for Language Model Updating by Mitigating LM-Logical Discrepancy
Large Language Models~(LLMs) struggle with providing current information due to the outdated pre-training data. Existing methods for updating LLMs, such as knowledge editing and continual fine-tuning, have significant drawbacks in generalizability of new information and the requirements on structured updating corpus. We identify the core challenge behind these drawbacks: the LM-logical discrepancy featuring the difference between language modeling probabilities and logical probabilities. To eva…

This https://arxiv.org/abs/2308.10743 has been replaced.
link: https://scholar.google.com/scholar?q=a

Enhancing Adversarial Attacks: The Similar Target Method
Deep neural networks are vulnerable to adversarial examples, posing a threat to the models' applications and raising security concerns. An intriguing property of adversarial examples is their strong transferability. Several methods have been proposed to enhance transferability, including ensemble attacks which have demonstrated their efficacy. However, prior approaches simply average logits, probabilities, or losses for model ensembling, lacking a comprehensive analysis of how and why model ens…

Mediated probabilities of causation
Max Rubinstein, Maria Cuellar, Daniel Malinsky
https://arxiv.org/abs/2404.07397 https://arxiv.org…

Mediated probabilities of causation
We propose a set of causal estimands that we call ``the mediated probabilities of causation.'' These estimands quantify the probabilities that an observed negative outcome was induced via a mediating pathway versus a direct pathway in a stylized setting involving a binary exposure or intervention, a single binary mediator, and a binary outcome. We outline a set of conditions sufficient to identify these effects given observed data, and propose a doubly-robust projection based estimation strateg…

This https://arxiv.org/abs/2210.09095 has been replaced.
link: https://scholar.google.com/scholar?q=a

Qualitative reasoning in a two-layered framework
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In the first part, we formalise reasoning with the qualitative counterparts of capacities, belief functions, and probabilities, within the framework of two-layered logics. Namely, we provide two-layered logics built over the classical propositional logic using a u…

A General Theory of Static Response for Markov Jump Processes
Timur Aslyamov, Massimiliano Esposito
https://arxiv.org/abs/2402.13990 https://

A General Theory of Static Response for Markov Jump Processes
We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they are constrained by the graph topology (i.e. the incidence matrix) by deriving response relations (i.e. linear constraints linking the different responses) and topology-dependent bounds. For unicyclic networks, all scaled current sensitivities are between zero …

This https://arxiv.org/abs/2205.08800 has been replaced.
link: https://scholar.google.com/scholar?q=a

Connection Probabilities of Multiple FK-Ising Interfaces
We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight $q \in [1,4)$. Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are …

Mediated probabilities of causation
Max Rubinstein, Maria Cuellar, Daniel Malinsky
https://arxiv.org/abs/2404.07397 https://arxiv.org…

Mediated probabilities of causation
We propose a set of causal estimands that we call ``the mediated probabilities of causation.'' These estimands quantify the probabilities that an observed negative outcome was induced via a mediating pathway versus a direct pathway in a stylized setting involving a binary exposure or intervention, a single binary mediator, and a binary outcome. We outline a set of conditions sufficient to identify these effects given observed data, and propose a doubly-robust projection based estimation strateg…

Revisiting series expansions of neutrino oscillation and decay probabilities in matter
Jesper Grönroos, Tommy Ohlsson, Sampsa Vihonen
https://arXiv.org/abs/2401.16864

Revisiting series expansions of neutrino oscillation and decay probabilities in matter
We present analytic expressions for three-flavor neutrino oscillations in presence of invisible neutrino decay and matter effects. Using the well-known Cayley-Hamilton formalism, the leading-order terms are derived for oscillation probabilities in all major channels assuming the neutrino mass eigenstate $ν_3$ to decay into sterile neutrinos. Our work extends and complements previous studies utilizing the Cayley-Hamilton theorem, providing the series expansions for $ν_e \rightarrow ν_e$, $ν_…

A Nonlocality Anomaly and Extended Semiquantum Games
Yiruo Lin
https://arxiv.org/abs/2402.08168 https://arxiv.org/pdf/2402.08168

A Nonlocality Anomaly and Extended Semiquantum Games
A nonlocality anomaly in which a partially entangled state can outperform a maximally entangled state in a task exploiting nonlocality and several ways to remove the anomaly are discussed. A necessary condition for the anomaly to occur is given in terms of joint probabilities of local measurements. By extending semiquantum games to include classical communication, the anomaly is shown to be removed with respect to semiquantum probabilities.

Logistic-beta processes for modeling dependent random probabilities with beta marginals
Changwoo J. Lee, Alessandro Zito, Huiyan Sang, David B. Dunson
https://arxiv.org/abs/2402.07048

Logistic-beta processes for modeling dependent random probabilities with beta marginals
The beta distribution serves as a canonical tool for modeling probabilities and is extensively used in statistics and machine learning, especially in the field of Bayesian nonparametrics. Despite its widespread use, there is limited work on flexible and computationally convenient stochastic process extensions for modeling dependent random probabilities. We propose a novel stochastic process called the logistic-beta process, whose logistic transformation yields a stochastic process with common b…

This https://arxiv.org/abs/2303.09198 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Large deviations for triangles in scale-free random graphs
We provide large deviations estimates for the upper tail of the number of triangles in scale-free inhomogeneous random graphs where the degrees have power law tails with index $-α, α\in (1,2)$. We show that upper tail probabilities for triangles undergo a phase transition. For $α<4/3$, the upper tail is caused by many vertices of degree of order $n$, and this probability is semi-exponential. In this regime, additional triangles consist of two hubs. For $α>4/3$ on the other hand, the upper t…

This https://arxiv.org/abs/2307.08111 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Electron Scattering at a Potential Temporal Step Discontinuity
We solve the problem of electron scattering at a potential temporal step discontinuity. We show that the Schrodinger equation cannot account for scattering in this problem, necessitating resort to the Dirac equation, and that breaking gauge symmetry requires a vector potential, a scalar potential inducing only Aharonov-Bohm type energy transitions. We derive the scattering probabilities, of later forward and backward nature, with the later-backward wave being a relativistic effect, and compare …

This https://arxiv.org/abs/2205.02734 has been replaced.
link: https://scholar.google.com/scholar?q=a

Percolation critical probabilities of matching lattice-pairs
A necessary and sufficient condition is established for the strict inequality $p_c(G_*)

On the Independence Assumption in Neurosymbolic Learning
Emile van Krieken, Pasquale Minervini, Edoardo M. Ponti, Antonio Vergari
https://arxiv.org/abs/2404.08458

On the Independence Assumption in Neurosymbolic Learning
State-of-the-art neurosymbolic learning systems use probabilistic reasoning to guide neural networks towards predictions that conform to logical constraints over symbols. Many such systems assume that the probabilities of the considered symbols are conditionally independent given the input to simplify learning and reasoning. We study and criticise this assumption, highlighting how it can hinder optimisation and prevent uncertainty quantification. We prove that loss functions bias conditionally …

This https://arxiv.org/abs/2307.07898 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

A Graph-Prediction-Based Approach for Debiasing Underreported Data
We present a novel Graph-based debiasing Algorithm for Underreported Data (GRAUD) aiming at an efficient joint estimation of event counts and discovery probabilities across spatial or graphical structures. This innovative method provides a solution to problems seen in fields such as policing data and COVID-$19$ data analysis. Our approach avoids the need for strong priors typically associated with Bayesian frameworks. By leveraging the graph structures on unknown variables $n$ and $p$, our meth…

This https://arxiv.org/abs/2205.02734 has been replaced.
link: https://scholar.google.com/scholar?q=a

Percolation critical probabilities of matching lattice-pairs
A necessary and sufficient condition is established for the strict inequality $p_c(G_*)

This https://arxiv.org/abs/2401.13889 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Can quantum theory be underpinned by a non-local hidden variable theory ?
In this paper we consider the description by a general Bell-type non-local hidden variable theory (NLHVT) of bipartite quantum states with two observables per sub-system. We derive Bell inequalities of the Collins-Gisin.-Liden-Massar-Popescu (CGLMP) type which involve combinations of the probabilities of related outcomes for measurements for the four pairs of sub-system observables. It is shown that the corresponding quantum theory expressions violate the Bell inequalities in the case of the ma…

Compressibility and Stochastic Stability of Monotone Markov Chain
Sergey Foss, Michael Scheutzow
https://arxiv.org/abs/2403.15259 https://

Compressibility and Stochastic Stability of Monotone Markov Chain
For a stochastically monotone Markov chain taking values in a Polish space, we present a number of conditions for existence and for uniqueness of its stationary regime, as well as for closeness of its transient trajectories. In particular, we generalise a basic result by Bhattacharya and Majumdar (2007) where a certain form of mixing, or swap condition was assumed uniformly over the state space. We do not rely on continuity properties of transition probabilities.

On the Independence Assumption in Neurosymbolic Learning
Emile van Krieken, Pasquale Minervini, Edoardo M. Ponti, Antonio Vergari
https://arxiv.org/abs/2404.08458

On the Independence Assumption in Neurosymbolic Learning
State-of-the-art neurosymbolic learning systems use probabilistic reasoning to guide neural networks towards predictions that conform to logical constraints over symbols. Many such systems assume that the probabilities of the considered symbols are conditionally independent given the input to simplify learning and reasoning. We study and criticise this assumption, highlighting how it can hinder optimisation and prevent uncertainty quantification. We prove that loss functions bias conditionally …

This https://arxiv.org/abs/2403.12941 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotics for Sinaĭ excursions
We study a class of random polymers, introduced by Sina\uı, which are related to persistence probabilities in integrated simple random walk bridges. We find the precise asymptotics of these probabilities, and describe their combinatorics, using limit theory for infinitely divisible distributions, and the number-theoretic subset counting formulas of von Sterneck from the early 1900s. Our results sharpen estimates by Aurzada, Dereich and Lifshits, and respond to a conjecture of Caravenna and Deu…

Entry-Specific Bounds for Low-Rank Matrix Completion under Highly Non-Uniform Sampling
Xumei Xi, Christina Lee Yu, Yudong Chen
https://arxiv.org/abs/2403.00184

Entry-Specific Bounds for Low-Rank Matrix Completion under Highly Non-Uniform Sampling
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying probabilities, potentially with different asymptotic scalings. We show that under structured sampling probabilities, it is often better and sometimes optimal to run estimation algorithms on a smaller submatrix rather than the entire matrix. In particular, we prove error …

This https://arxiv.org/abs/2309.06429 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Efficient Inference on High-Dimensional Linear Models with Missing Outcomes
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias correction term based on the weighted residuals of the Lasso regression. The weights depend on estimates of the missingness probabilities (propensity scores) and solve a convex optimization program that trades off bias and variance optimally. Provided that the…

Asymptotics for Sina\u{i} excursions
Serte Donderwinkel, Brett Kolesnik
https://arxiv.org/abs/2403.12941 https://arxiv.org/pdf/2403.1…

Asymptotics for Sinaĭ excursions
We study a class of random polymers, introduced by Sina\uı, which are related to persistence probabilities in integrated simple random walk bridges. We find the precise asymptotics of these probabilities, and describe their combinatorics, using limit theory for infinitely divisible distributions, and the number-theoretic subset counting formulas of von Sterneck from the early 1900s. Our results sharpen estimates by Aurzada, Dereich and Lifshits, and respond to a conjecture of Caravenna and Deu…

De-Biasing the Bias: Methods for Improving Disparity Assessments with Noisy Group Measurements
Solvejg Wastvedt, Joshua Snoke, Denis Agniel, Julie Lai, Marc N. Elliott, Steven C. Martino
https://arxiv.org/abs/2402.13391

De-Biasing the Bias: Methods for Improving Disparity Assessments with Noisy Group Measurements
Health care decisions are increasingly informed by clinical decision support algorithms, but these algorithms may perpetuate or increase racial and ethnic disparities in access to and quality of health care. Further complicating the problem, clinical data often have missing or poor quality racial and ethnic information, which can lead to misleading assessments of algorithmic bias. We present novel statistical methods that allow for the use of probabilities of racial/ethnic group membership in a…

Entry-Specific Bounds for Low-Rank Matrix Completion under Highly Non-Uniform Sampling
Xumei Xi, Christina Lee Yu, Yudong Chen
https://arxiv.org/abs/2403.00184

Entry-Specific Bounds for Low-Rank Matrix Completion under Highly Non-Uniform Sampling
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying probabilities, potentially with different asymptotic scalings. We show that under structured sampling probabilities, it is often better and sometimes optimal to run estimation algorithms on a smaller submatrix rather than the entire matrix. In particular, we prove error …

This https://arxiv.org/abs/2402.17123 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Theory-Independent Realism
The distinctive features of quantum mechanics, which set it apart from other physical theories, challenge our notions of realism. Recovering realism from purely philosophical grounds, a quantitative and operational criterion was proposed in the past, but solely for the context of quantum mechanics. We use a framework of generalized probabilistic theories to expand the notion of realism for a theory-independent context, providing a criterion uniquely based on the probabilities assigned to measur…

Horseshoe Priors for Sparse Dirichlet-Multinomial Models
Yuexi Wang, Nicholas G. Polson
https://arxiv.org/abs/2402.09583 https://arxi…

Horseshoe Priors for Sparse Dirichlet-Multinomial Models
Bayesian inference for Dirichlet-Multinomial (DM) models has a long and important history. The concentration parameter $α$ is pivotal in smoothing category probabilities within the multinomial distribution and is crucial for the inference afterward. Due to the lack of a tractable form of its marginal likelihood, $α$ is often chosen ad-hoc, or estimated using approximation algorithms. A constant $α$ often leads to inadequate smoothing of probabilities, particularly for sparse compositional co…

This https://arxiv.org/abs/2112.10022 has been replaced.
link: https://scholar.google.com/scholar?q=a

Probabilities and certainties within a causally symmetric model
This paper is concerned with the causally symmetric version of the familiar de Broglie-Bohm interpretation, this version allowing the spacelike nonlocality and the configuration space ontology of the original model to be avoided via the addition of retrocausality. Two different features of this alternative formulation are considered here. With regard to probabilities, it is shown that the model provides a derivation of the Born rule identical to that in Bohm's original formulation. This derivat…

This https://arxiv.org/abs/2312.17406 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sampling probabilities, diffusions, ancestral graphs, and duality under strong selection
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the sampling probability, a crucial quantity in inference. Under a finite-allele mutation model, with possibly parent-dependent mutation, we consider the asymptotic regime where the selective advantage of one allele grows to infinity, while the other parameters r…

Investigating the Effect of Noise on the Training Performance of Hybrid Quantum Neural Networks
Muhammad Kashif, Emman Sychiuco, Muhammad Shafique
https://arxiv.org/abs/2402.08523

Investigating the Effect of Noise on the Training Performance of Hybrid Quantum Neural Networks
In this paper, we conduct a comprehensively analyze the influence of different quantum noise gates, including Phase Flip, Bit Flip, Phase Damping, Amplitude Damping, and the Depolarizing Channel, on the performance of HyQNNs. Our results reveal distinct and significant effects on HyQNNs training and validation accuracies across different probabilities of noise. For instance, the Phase Flip gate introduces phase errors, and we observe that HyQNNs exhibit resilience at higher probability (p = 1.0…

This https://arxiv.org/abs/2402.09583 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Horseshoe Priors for Sparse Dirichlet-Multinomial Models
Bayesian inference for Dirichlet-Multinomial (DM) models has a long and important history. The concentration parameter $α$ is pivotal in smoothing category probabilities within the multinomial distribution and is crucial for the inference afterward. Due to the lack of a tractable form of its marginal likelihood, $α$ is often chosen in an ad-hoc manner, or estimated using approximation algorithms. A constant $α$ often leads to inadequate smoothing of probabilities, particularly for sparse com…

This https://arxiv.org/abs/2211.04505 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry
Variational quantum eigensolvers (VQEs) are leading candidates to demonstrate near-term quantum advantage. Here, we conduct density-matrix simulations of leading gate-based VQEs for a range of molecules. We numerically quantify their level of tolerable depolarizing gate-errors. We find that: (i) The best-performing VQEs require gate-error probabilities between $10^{-6}$ and $10^{-4}$ ( $10^{-4}$ and $10^{-2}$ with error mitigation) to predict, within chemical accuracy, ground-state energies of …

This https://arxiv.org/abs/2111.10979 has been replaced.
link: https://scholar.google.com/scholar?q=a

Renormalization of crossing probabilities in the dilute Potts model
A recent paper due to Duminil-Copin and Tassion from 2019 introduces a novel argument for obtaining estimates on horizontal crossing probabilities of the random cluster model, in which a range of four possible behaviors is established. To apply the novel renormalization of crossing probabilities that the authors propose can be studied in other models of interest that are not self-dual, we collect results to formulate vertical and horizontal strip, and renormalization, inequalities for the dilut…