arXiv research

Guaranteed bounds for posterior inference in probabilistic programs.

The resilience of low-degree Rademacher chaos is studied, providing probabilistic lower bounds.

Study probabilistic category and complexity bounds, comparing with classical invariants.

Extends branch and bound for probabilistic neural network verification.

Unified framework for learning flexible probabilistic programs using DPP and PAC-Bayes bounds.

PAC-Bayesian bounds for MLPs with cross entropy loss validated.

Unified framework for differentiable graph partitioning with probabilistic cuts.

Estimates chirp signal frequencies using probabilistic models.

Paper develops probabilistic bounds for a stochastic gradient algorithm in non-convex problems.

This paper improves DNN generalization by accurately estimating mutual information.

New bound on partition function proves Kähler-Einstein stability.

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 Kullback-Leibler divergence that allows understanding methods that penalize the …

The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.

We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in…

A new error bound improves safety in Bayesian optimization.

Deep learning improves probabilistic PPDE solution accuracy.

Bayesian optimization tackles expensive discrete and mixed parameter spaces.

We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal quantization, and learning theory, we derive new probabilistic bounds for the per…

We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. W…

The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a generalization that allows a limited notion of arbitrage in the market while still…

The paper gives bounds for how long it takes for gossip protocols to spread information in networks.

We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence…

The paper studies batch decompositions of random datasets with probabilistic similarity constraints.

Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.

With deep neural networks providing state-of-the-art machine learning models for numerous machine learning tasks, quantifying the robustness of these models has become an important area of research. However, most of the research literature merely focuses on the \textit{worst-case} setting where the input of the neural …

The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to take place at a finite number of occasions but not bounded in number nor necessari…

New method calibrates DPMs to improve likelihood bounds.

Unified framework for information-theoretic bounds on learning algorithms.

We consider a problem of stochastic online learning with general probabilistic graph feedback, where each directed edge in the feedback graph has probability $p_{ij}$. Two cases are covered. (a) The one-step case, where after playing arm $i$ the learner observes a sample reward feedback of arm $j$ with independent prob…

A new diffusion model tackles brightness issues with a probabilistic approach.

High-quality image synthesis with diffusion models, achieving state-of-the-art FID score.

Active learning algorithms propose which unlabeled objects should be queried for their labels to improve a predictive model the most. We study active learners that minimize generalization bounds and uncover relationships between these bounds that lead to an improved approach to active learning. In particular we show th…

Paper introduces DMPMs for efficient discrete data generation with sharp convergence bounds.

New probabilistic invariants bound classical topological complexity and category.

Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c >= rank(A) columns depend on the right singular vector matrix of A. For a Monte-…

Study probabilistic safety of BNNs under adversarial attacks.

Paper analyzes GCNN sensitivity to probabilistic graph perturbations.

Statistical model checking for PCTL on MDPs using reinforcement learning.

Efficient RL in PRMs with improved regret bound.

New algorithm for contextual combinatorial bandits with probabilistic arm triggering.

We study combinatorial multi-armed bandit with probabilistically triggered arms (CMAB-T) and semi-bandit feedback. We resolve a serious issue in the prior CMAB-T studies where the regret bounds contain a possibly exponentially large factor of $1/p^*$, where $p^*$ is the minimum positive probability that an arm is trigg…

New bounds on AE success probability in GP models.

Improved bounds for proximal gradient algorithms with computational errors.

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the…

We consider an active learning setting where the algorithm has access to a large pool of unlabeled data and a small pool of labeled data. In each iteration, the algorithm chooses few unlabeled data points and obtains their labels from an oracle. In this paper, we consider a probabilistic querying procedure to choose th…

We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is intractable, we show how to compute upper and lower bounds on many probabilities of intere…

We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and on the Good-Turing missing mass estimator. We prove two different regret bounds on t…

Optimizes pruning masks for neural networks using probabilistic fine-tuning and PAC-Bayes bounds.