This work considers methods for imposing sparsity in Bayesian regression with applications in nonlinear system identification. We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional regularization or thresholding to achieve sparse models. We then discuss two classes of methods, regularization based and thresholding based, which build on ARD to learn parsimonious solutions to linear problems. In the case of orthogonal covariates, we analytically demonstrate favorable performance with regards to learning a small set of active terms in a linear system with a sparse solution. Several example problems are presented to compare the set of proposed methods in terms of advantages and limitations to ARD in bases with hundreds of elements. The aim of this paper is to analyze and understand the assumptions that lead to several algorithms and to provide theoretical and empirical results so that the reader may gain insight and make more informed choices regarding sparse Bayesian regression.

We consider the problem of discovering the causal process that generated a collection of datasets. We assume that all these datasets were generated by unknown sparse interventions on a structural causal model (SCM) $G$, that we want to identify. Recently, Bengio et al. (2020) argued that among all SCMs, $G$ is the fastest to adapt from one dataset to another, and proposed a meta-learning criterion to identify the causal direction in a two-variable SCM. While the experiments were promising, the theoretical justification was incomplete. Our contribution is a theoretical investigation of the adaptation speed of simple two-variable SCMs. We use convergence rates from stochastic optimization to justify that a relevant proxy for adaptation speed is distance in parameter space after intervention. Using this proxy, we show that the SCM with the correct causal direction is advantaged for categorical and normal cause-effect datasets when the intervention is on the cause variable. When the intervention is on the effect variable, we provide a more nuanced picture which highlights that the fastest-to-adapt heuristic is not always valid. Code to reproduce experiments is available at https://github.com/remilepriol/causal-adaptation-speed

Traceability is a fundamental component of the modern software development process that helps to ensure properly functioning, secure programs. Due to the high cost of manually establishing trace links, researchers have developed automated approaches that draw relationships between pairs of textual software artifacts using similarity measures. However, the effectiveness of such techniques are often limited as they only utilize a single measure of artifact similarity and cannot simultaneously model (implicit and explicit) relationships across groups of diverse development artifacts. In this paper, we illustrate how these limitations can be overcome through the use of a tailored probabilistic model. To this end, we design and implement a HierarchiCal PrObabilistic Model for SoftwarE Traceability (Comet) that is able to infer candidate trace links. Comet is capable of modeling relationships between artifacts by combining the complementary observational prowess of multiple measures of textual similarity. Additionally, our model can holistically incorporate information from a diverse set of sources, including developer feedback and transitive (often implicit) relationships among groups of software artifacts, to improve inference accuracy. We conduct a comprehensive empirical evaluation of Comet that illustrates an improvement over a set of optimally configured baselines of $\approx$14% in the best case and $\approx$5% across all subjects in terms of average precision. The comparative effectiveness of Comet in practice, where optimal configuration is typically not possible, is likely to be higher. Finally, we illustrate Comets potential for practical applicability in a survey with developers from Cisco Systems who used a prototype Comet Jenkins plugin.

Solar activity It is vital to accurately predict solar activity, in order to decrease the plausible damage of electronic equipment in the event of a large high-intensity solar eruption. Recently, we have proposed BELFIS (Brain Emotional Learning-based Fuzzy Inference System) as a tool for the forecasting of chaotic systems. The structure of BELFIS is designed based on the neural structure of fear conditioning. The function of BELFIS is implemented by assigning adaptive networks to the components of the BELFIS structure. This paper especially focuses on performance evaluation of BELFIS as a predictor by forecasting solar cycles 16 to 24. The performance of BELFIS is compared with other computational models used for this purpose, and in particular with adaptive neuro-fuzzy inference system (ANFIS).

Many real data sets contain features (variables) whose distribution is far from normal (gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box-Cox and Yeo-Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose an automatic preprocessing technique that is robust against such outliers, which transforms the data to central normality. It compares favorably to existing techniques in an extensive simulation study and on real data.

In this work we provide a review of basic ideas and novel developments about Conformal Prediction -- an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions -- that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case. The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.

In this paper, we present a Bayesian approach for finite mixture models based on three-parameter bivariate Beta distributions. The estimation of the parameters is based on the Monte Carlo simulation technique of Gibbs sampling mixed with a Metropolis-Hastings step. The performance of our Bayesian algorithm is verified by several synthetic datasets and in the end, the feasibility of the proposed method is demonstrated by experimenting on some real datasets in which, the results are compared with those obtained by implementing the same approach using Gaussian mixture model.

Modeling high-dimensional multivariate distributions is a computationally challenging task. Bayesian networks have been successfully used to reduce the complexity and simplify the problem with discrete variables. However, it lacks of a general model for continuous variables. In order to overcome this problem, Elidan (2010) proposed the model of copula bayesian networks (CBN) that reparametrizes bayesian networks with conditional copula functions. We propose a new learning algorithm for CBN based on a PC algorithm and a conditional independence test proposed by Bouezmarni, Rombouts, Taamouti (2009). This test being non-parametric, no model assumptions are made allowing it to be as general as possible. This algorithm is compared on generated data with the score based method proposed by Elidan (2010)}. Not only it proves to be faster, but also it generalizes well on data generated from distributions far from the gaussian model.

Bayesian networks (BNs) encode conditional independence to avoid combinatorial explosion on the number of variables, but are subject to exponential growth of space and inference time on the number of causes per effect variable. Among space-efficient local models, we focus on the Non-Impeding Noisy-AND Tree (NIN-AND Tree or NAT) models due to their multiple merits, and on NAT-modeled BNs where each multi-parent variable family may be encoded as a NAT-model. Although BN inference is generally exponential on treewidth, inference is tractable with NAT-modeled BNs of high treewidth and low density. In this work, we present the first study to learn NAT-modeled BNs from data. We apply the MDL principle to learning NAT-modeled BNs by developing a corresponding scoring function, and we couple it with heuristic structure search. We show that when data satisfy NAT causal independence, and high treewidth, low density structure, learning underlying NAT modeled BNs is feasible.

Bayesian inference is crucial to challenging scenarios that involve complex probabilistic models, which are usually intractable. In this work, we develop an expectation propagation approach to learn finite mixture models of EDCMs. The EDCM (Elkan 2006) is an exponential-family approximation to the widely used Dirichlet Compound Multinomial distribution and has been shown to offer excellent modeling capabilities in the case of sparse count data. Expectation propagation is a deterministic approach that provides accurate approximations to the full posterior and allows to include prior beliefs in the model as opposed to the maximum-likelihood method, which provides point estimates only. We evaluate the efficiency of our framework on several datasets for sentiment analysis and shape recognition. Our proposed model shows comparable to superior results to other approaches in the literature.