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We consider stochastic optimization problems with the dual tasks of (i) effectively finding the optimizer and (ii) reliably conducting statistical inference for the optimal objective function value. We find that classical simulation…
The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density $\pi$, when we are only able to estimate an unnormalized version of $\pi$…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
This paper introduces a novel ranking of statistical experiments, the linear-Blackwell (LB) order, which can equivalently be characterized by (i) the dispersion of the induced posterior and likelihood ratios in the sense of the linear…
Under reasonable algebraic assumptions and under an infinite second order moment assumption, we show that the logarithm of the norm (log-norm) of a product of random i.i.d. matrices with entries in $\mathbb{R}$ or in any other local field…
In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant…
The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…
We initiate a study of locally decodable codes with randomized encoding. Standard locally decodable codes are error correcting codes with a deterministic encoding function and a randomized decoding function, such that any desired message…
Learning from Label Proportions (LLP) is a learning setting, where the training data is provided in groups, or "bags", and only the proportion of each class in each bag is known. The task is to learn a model to predict the class labels of…
Lossy channel systems (LCSs) are systems of finite state automata that communicate via unreliable unbounded fifo channels. In order to circumvent the undecidability of model checking for nondeterministic LCSs, probabilistic models have been…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…
The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension…
The execution of Large Language Models (LLMs) has been shown to produce nondeterministic results when run on Graphics Processing Units (GPUs), even when they are configured to produce deterministic results. This is due to the finite…
Determinantal Point Processes (DPPs) are a widely used probabilistic model for negatively correlated sets. DPPs have been successfully employed in Machine Learning applications to select a diverse, yet representative subset of data. In…
This paper considers robot motion planning under temporal logic constraints in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The uncertainty in a map distribution presents a great challenge for…
We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the…
The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…
Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the…
In recent years, several probabilistic techniques have been applied to various debugging problems. However, most existing probabilistic debugging systems use relatively simple statistical models, and fail to generalize across multiple…