Related papers: Lower Bounds for Possibly Divergent Probabilistic …
The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained…
We study downward deviations of the maximum local time of the discrete-time simple random walk on $\mathbb{Z}^d$, $d\ge 3$. In our previous paper \cite{li2026ldmaxlocal}, the corresponding upper bound was established, while the matching…
In [1] a syndrome counting based upper bound on the minimum distance of regular binary LDPC codes is given. In this paper we extend the bound to the case of irregular and generalized LDPC codes over GF(q). The comparison to the lower bound…
Probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating…
We present a coupled decreasing sequence of random walks on $ \mathbb Z $ that dominates the edge process of oriented-bond percolation in two dimensions. Using the concept of "random walk in a strip ", we construct an algorithm that…
In this paper, two new classes of lower bounds on the probability of error for $m$-ary hypothesis testing are proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP)…
We propose a new method to approximate the posterior distribution of probabilistic programs by means of computing guaranteed bounds. The starting point of our work is an interval-based trace semantics for a recursive, higher-order…
This paper introduces a new technique for quantifying the approximation error of a broad class of probabilistic inference programs, including ones based on both variational and Monte Carlo approaches. The key idea is to derive a subjective…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…
The exact lower bound on the probability of the occurrence of exactly one of $n$ random events each of probability $p$ is obtained.
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…
The paper presents two results. The first one provides separate conditions for the upper and lower estimate of the distribution of the exit time from balls of a random walk on a weighted graph. The main result of the paper is that the lower…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
We consider a symmetric random walk on the $\nu$-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction…
In this paper we find an upper bound for the probability that a $3$ dimensional simple random walk covers each point in a nearest neighbor path connecting 0 and the boundary of an $L_1$ ball of radius $N$. For $d\ge 4$, it has been shown in…
This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost-sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
With the objective of developing computational methods for stability analysis of switched systems, we consider the problem of finding the minimal lower bounds on average dwell-time that guarantee global asymptotic stability of the origin.…
In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where…