Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and b) generative methods. The latter, more widely known as Bayesian methods, enable uncertainty evaluation w.r.t. the performed predictions. Furthermore, they can better exploit related prior information and naturally introduce robustness into the model, due to their unique capacity to marginalize out uncertainties related to the parameter estimates. Moreover, hyper-parameters associated with the adopted priors can be learnt via the training data. To implement sparsity-aware learning, the crucial point lies in the choice of the function regularizer for discriminative methods and the choice of the prior distribution for Bayesian learning. Over the last decade or so, due to the intense research on deep learning, emphasis has been put on discriminative techniques. However, a come back of Bayesian methods is taking place that sheds new light on the design of deep neural networks, which also establish firm links with Bayesian models and inspire new paths for unsupervised learning, such as Bayesian tensor decomposition. The goal of this article is two-fold. First, to review, in a unified way, some recent advances in incorporating sparsity-promoting priors into three highly popular data modeling tools, namely deep neural networks, Gaussian processes, and tensor decomposition. Second, to review their associated inference techniques from different aspects, including: evidence maximization via optimization and variational inference methods. Challenges such as small data dilemma, automatic model structure search, and natural prediction uncertainty evaluation are also discussed. Typical signal processing and machine learning tasks are demonstrated.

This paper addresses a data integration problem: given several mutually consistent datasets each of which measures a subset of the variables of interest, how can one construct a probabilistic model that fits the data and gives reasonable answers to questions which are under-determined by the data? Here we show how to obtain a Bayesian network model which represents the unique probability function that agrees with the probability distributions measured by the datasets and otherwise has maximum entropy. We provide a general algorithm, OBN-cDS, which offers substantial efficiency savings over the standard brute-force approach to determining the maximum entropy probability function. Furthermore, we develop modifications to the general algorithm which enable further efficiency savings but which are only applicable in particular situations. We show that there are circumstances in which one can obtain the model (i) directly from the data; (ii) by solving algebraic problems; and (iii) by solving relatively simple independent optimisation problems.

Last week, I saw a nice presentation on Probabilistic Programming from a student in Iran (link below). I am interested in this subject for my teaching at the #universityofoxford. In this post, I provide a brief introduction to Probabilistic programming. Probabilistic programming is a programming paradigm designed to implement and solve probabilistic models. They unite probabilistic modeling and traditional general-purpose programming.

A wide range of modern artificial intelligence challenges ca n be cast as Reinforcement Learning (RL) problems under partial observability, in which agents learn to make a sequence of decisions despite lacking complete information about the underlying state of system. For example, in robotics the agent has to cope with noisy sensors, occlusions, and unk nown dynamics ( Akkaya et al., 2019), while in imperfect information games the player makes only l ocal observations ( Vinyals et al., 2019; Brown and Sandholm, 2019). Further applications of partially observable RL include autonomous driving ( Levinson et al., 2011), resource allocation ( Bower and Gilbert, 2005), medical diagnostic systems ( Hauskrecht and Fraser, 2000), recommendation ( Li et al., 2010), business management ( De Brito and Van Der Laan, 2009), etc. As such, learning and acting under partial observabi lity has been an important topic in operation research, control, and machine learning. Because of the non-Markovian nature of the observations, le arning and planning in partially observable environments requires an agent to maintain memory and possibly reason about beliefs over the states, all while exploring to collect information about the environment. As such, partial observability can significantly complicate learni ng and planning under uncertainty. While practical RL systems have succeeded in a set of partially obs ervable problems including Poker ( Brown and Sandholm, 2019), Starcraft ( Vinyals et al., 2019) and certain robotic tasks ( Cassandra et al., The author emails are {qinghual, alan.chung,

When starting out with Data Science, there is so much to learn it can become quite overwhelming. This guide will help aspiring data scientists and machine learning engineers gain better knowledge and experience. I will list different types of machine learning algorithms, which can be used with both Python and R. Linear Regression is the simplest Machine learning algorithm that branches off from Supervised Learning. It is primarily used to solve regression problems and make predictions on continuous dependent variables with the knowledge from independent variables. The goal of Linear Regression is to find the line of best fit, which can help predict the output for continuous dependent variables.

Multi-defender Stackelberg Security Games (MSSG) have recently gained increasing attention in the literature. However, the solutions offered to date are highly sensitive, wherein even small perturbations in the attacker's utility or slight uncertainties thereof can dramatically change the defenders' resulting payoffs and alter the equilibrium. In this paper, we introduce a robust model for MSSGs, which admits solutions that are resistant to small perturbations or uncertainties in the game's parameters. First, we formally define the notion of robustness, as well as the robust MSSG model. Then, for the non-cooperative setting, we prove the existence of a robust approximate equilibrium in any such game, and provide an efficient construction thereof. For the cooperative setting, we show that any such game admits a robust approximate alpha-core, provide an efficient construction thereof, and prove that stronger types of the core may be empty. Interestingly, the robust solutions can substantially increase the defenders' utilities over those of the non-robust ones.

The Expectation-Maximization (EM) algorithm has been predominantly used to approximate the maximum likelihood estimation of the location-scale Gaussian mixtures. However, when the models are over-specified, namely, the chosen number of components to fit the data is larger than the unknown true number of components, EM needs a polynomial number of iterations in terms of the sample size to reach the final statistical radius; this is computationally expensive in practice. The slow convergence of EM is due to the missing of the locally strong convexity with respect to the location parameter on the negative population log-likelihood function, i.e., the limit of the negative sample log-likelihood function when the sample size goes to infinity. To efficiently explore the curvature of the negative log-likelihood functions, by specifically considering two-component location-scale Gaussian mixtures, we develop the Exponential Location Update (ELU) algorithm. The idea of the ELU algorithm is that we first obtain the exact optimal solution for the scale parameter and then perform an exponential step-size gradient descent for the location parameter. We demonstrate theoretically and empirically that the ELU iterates converge to the final statistical radius of the models after a logarithmic number of iterations. To the best of our knowledge, it resolves the long-standing open question in the literature about developing an optimization algorithm that has optimal statistical and computational complexities for solving parameter estimation even under some specific settings of the over-specified Gaussian mixture models.

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN stemming from modeling errors and measurement uncertainty. We consider aleatoric uncertainty in the form of probabilistic links and noise in feature vector of nodes, while epistemic uncertainty is incorporated via a probability distribution over the model parameters. We propose a unified approach to treat both sources of uncertainty in a Bayesian framework, where Assumed Density Filtering is used to quantify aleatoric uncertainty and Monte Carlo dropout captures uncertainty in model parameters. Finally, the two sources of uncertainty are aggregated to estimate the total uncertainty in predictions of a GNN. Results in the real-world datasets demonstrate that the Bayesian model performs at par with a frequentist model and provides additional information about predictions uncertainty that are sensitive to uncertainties in the data and model.

Deep neural networks (DNNs) with noisy weights, which we refer to as noisy neural networks (NoisyNNs), arise from the training and inference of DNNs in the presence of noise. NoisyNNs emerge in many new applications, including the wireless transmission of DNNs, the efficient deployment or storage of DNNs in analog devices, and the truncation or quantization of DNN weights. This paper studies a fundamental problem of NoisyNNs: how to reconstruct the DNN weights from their noisy manifestations. While all prior works relied on the maximum likelihood (ML) estimation, this paper puts forth a denoising approach to reconstruct DNNs with the aim of maximizing the inference accuracy of the reconstructed models. The superiority of our denoiser is rigorously proven in two small-scale problems, wherein we consider a quadratic neural network function and a shallow feedforward neural network, respectively. When applied to advanced learning tasks with modern DNN architectures, our denoiser exhibits significantly better performance than the ML estimator. Consider the average test accuracy of the denoised DNN model versus the weight variance to noise power ratio (WNR) performance. When denoising a noisy ResNet34 model arising from noisy inference, our denoiser outperforms ML estimation by up to 4.1 dB to achieve a test accuracy of 60%.When denoising a noisy ResNet18 model arising from noisy training, our denoiser outperforms ML estimation by 13.4 dB and 8.3 dB to achieve test accuracies of 60% and 80%, respectively.

Principled Bayesian deep learning (BDL) does not live up to its potential when we only focus on marginal predictive distributions (marginal predictives). Recent works have highlighted the importance of joint predictives for (Bayesian) sequential decision making from a theoretical and synthetic perspective. We provide additional practical arguments grounded in real-world applications for focusing on joint predictives: we discuss online Bayesian inference, which would allow us to make predictions while taking into account additional data without retraining, and we propose new challenging evaluation settings using active learning and active sampling. These settings are motivated by an examination of marginal and joint predictives, their respective cross-entropies, and their place in offline and online learning. They are more realistic than previously suggested ones, building on work by Wen et al. (2021) and Osband et al. (2022), and focus on evaluating the performance of approximate BNNs in an online supervised setting. Initial experiments, however, raise questions on the feasibility of these ideas in high-dimensional parameter spaces with current BDL inference techniques, and we suggest experiments that might help shed further light on the practicality of current research for these problems. Importantly, our work highlights previously unidentified gaps in current research and the need for better approximate joint predictives.