Related papers: Towards Tsallis Fully Probabilistic Design

This work elaborates on the important problem of (1) designing optimal randomized routing policies for reaching a target node t from a source note s on a weighted directed graph G and (2) defining distance measures between nodes…

The robustness of fault detection algorithms against uncertainty is crucial in the real-world industrial environment. Recently, a new probabilistic design scheme called distributionally robust fault detection (DRFD) has emerged and received…

This paper provides a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative…

Probabilistic Latent Tensor Factorization (PLTF) is a recently proposed probabilistic framework for modelling multi-way data. Not only the common tensor factorization models but also any arbitrary tensor factorization structure can be…

The Kullback-Leibler (KL) divergence plays a central role in probabilistic machine learning, where it commonly serves as the canonical loss function. Optimization in such settings is often performed over the probability simplex, where the…

It is shown that distributions arising in Renyi-Tsallis maximum entropy setting are related to the Generalized Pareto Distributions (GPD) that are widely used for modeling the tails of distributions. The relevance of such modelization, as…

Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…

We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…

Federated learning (FL) has emerged as a widely adopted training paradigm for privacy-preserving machine learning. While the SGD-based FL algorithms have demonstrated considerable success in the past, there is a growing trend towards…

Decision-making under uncertainty is often considered in two stages: predicting the unknown parameters, and then optimizing decisions based on predictions. While traditional prediction-focused learning (PFL) treats these two stages…

Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a…

Federated Learning (FL) enables multiple clients to collaboratively train models without sharing raw data, but it is highly vulnerable to Byzantine attacks. Existing robust approaches can neutralize these threats but incur substantial…

In this paper, a sparse Markov decision process (MDP) with novel causal sparse Tsallis entropy regularization is proposed.The proposed policy regularization induces a sparse and multi-modal optimal policy distribution of a sparse MDP. The…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations…

Signal Temporal Logic (STL) specifications play a crucial role in defining complex temporal properties and behaviors in safety-critical cyber-physical systems (CPS). However, fault diagnosis (FD) and fault-tolerant control (FTC) for CPS…

Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…

A transformed primal-dual (TPD) flow is developed for a class of nonlinear smooth saddle point system. The flow for the dual variable contains a Schur complement which is strongly convex. Exponential stability of the saddle point is…

Real-world complex systems often comprise many distinct types of elements as well as many more types of networked interactions between elements. When the relative abundances of types can be measured well, we often observe heavy-tailed…