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The Forward-Forward (FF) algorithm was recently proposed as a local learning method to address the limitations of backpropagation (BP), offering biological plausibility along with memory-efficient and highly parallelized computational…

This paper offers a novel mathematical approach, the modified Fractional-order Steepest Descent Method (FSDM) for training BackPropagation Neural Networks (BPNNs); this differs from the majority of the previous approaches and as such. A…

We develop and analyze a broad family of stochastic/randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge…

Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…

A leading family of algorithms for state estimation in dynamic systems with multiple sub-states is based on particle filters (PFs). PFs often struggle when operating under complex or approximated modelling (necessitating many particles)…

The goal of Boolean Matrix Factorization (BMF) is to approximate a given binary matrix as the product of two low-rank binary factor matrices, where the product of the factor matrices is computed under the Boolean algebra. While the problem…

Particle filters (PFs) are powerful sampling-based inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and non-stationarity.…

Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…

In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Bayesian optimization (BO) is a popular framework to optimize black-box functions. In many applications, the objective function can be evaluated at multiple fidelities to enable a trade-off between the cost and accuracy. To reduce the…

The best current methods for exactly computing the number of satisfying assignments, or the satisfying probability, of Boolean formulas can be seen, either directly or indirectly, as building 'decision-DNNF' (decision decomposable negation…

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…

Bayesian networks (BNs) are attractive, because they are graphical and interpretable machine learning models. However, exact inference on BNs is time-consuming, especially for complex problems. To improve the efficiency, we propose a fast…

Recent advances in communications, mobile computing, and artificial intelligence have greatly expanded the application space of intelligent distributed sensor networks. This in turn motivates the development of generalized Bayesian…

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…

Bayesian Neural Networks (BNN) have emerged as a crucial approach for interpreting ML predictions. By sampling from the posterior distribution, data scientists may estimate the uncertainty of an inference. Unfortunately many inference…

This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…

Belief updating in Bayes nets, a well known computationally hard problem, has recently been approximated by several deterministic algorithms, and by various randomized approximation algorithms. Deterministic algorithms usually provide…

This paper proposes a deep neural network (DNN)-driven framework to address the longstanding generalization challenge in adaptive filtering (AF). In contrast to traditional AF frameworks that emphasize explicit cost function design, the…