Related papers: A Pre-Expectation Calculus for Probabilistic Sensi…
We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ($L^1$ Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently…
In the optimization under uncertainty, decision-makers first select a wait-and-see policy before any realization of uncertainty and then place a here-and-now decision after the uncertainty has been observed. Two-stage stochastic programming…
Solving partially observable Markov decision processes (POMDPs) with high dimensional and continuous observations, such as camera images, is required for many real life robotics and planning problems. Recent researches suggested machine…
We present a neural network verification toolbox to 1) assess the probability of satisfaction of a constraint, and 2) synthesize a set expansion factor to achieve the probability of satisfaction. Specifically, the tool box establishes with…
We present a definition of the distance between probability distributions. Our definition is based on the $L_1$ norm on space of probability measures. We compare our distance with the well-known Kullback-Leibler divergence and with the…
We relate the probability distribution of the work done on a statistical system under a sudden quench to the Lanczos coefficients corresponding to evolution under the post-quench Hamiltonian. Using the general relation between the moments…
In this paper, we develop approximate dynamic programming methods for stochastic systems modeled as Markov Decision Processes, given both soft performance criteria and hard constraints in a class of probabilistic temporal logic called…
Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…
Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…
Optimizing the expected values of probabilistic processes is a central problem in computer science and its applications, arising in fields ranging from artificial intelligence to operations research to statistical computing. Unfortunately,…
When an action potential is transmitted to a postsynaptic neuron, a small change in the postsynaptic neuron's membrane potential occurs. These small changes, known as a postsynaptic potentials (PSPs), are highly variable, and current models…
Sensitivity analysis is concerned with understanding how the model output depends on uncertainties (variances) in inputs and then identifies which inputs are important in contributing to the prediction imprecision. Uncertainty determination…
This work presents a new classifier that is specifically designed to be fully interpretable. This technique determines the probability of a class outcome, based directly on probability assignments measured from the training data. The…
Tempering is a popular tool in Bayesian computation, being used to transform a posterior distribution $p_1$ into a reference distribution $p_0$ that is more easily approximated. Several algorithms exist that start by approximating $p_0$ and…
Since the introduction of the Sliced Wasserstein distance in the literature, its simplicity and efficiency have made it one of the most interesting surrogate for the Wasserstein distance in image processing and machine learning. However,…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…