Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving approximate inference over the latent variables by minimizing a tight upper bound on the approximation gap. Given a discrete latent variable $Z$, the proposed approximation reduces inference complexity from $O(|Z|^c)$ to $O(|Z|)$. We use convex conjugates to determine this upper bound in a closed form and show that its addition to the optimization objective results in improved results for models assuming proportional hazards as in Survival Analysis.

Change-point detection (CPD) aims to locate abrupt transitions in the generative model of a sequence of observations. When Bayesian methods are considered, the standard practice is to infer the posterior distribution of the change-point locations. However, for complex models (high-dimensional or heterogeneous), it is not possible to perform reliable detection. To circumvent this problem, we propose to use a hierarchical model, which yields observations that belong to a lower-dimensional manifold. Concretely, we consider a latent-class model with an unbounded number of categories, which is based on the chinese-restaurant process (CRP). For this model we derive a continual learning mechanism that is based on the sequential construction of the CRP and the expectation-maximization (EM) algorithm with a stochastic maximization step. Our results show that the proposed method is able to recursively infer the number of underlying latent classes and perform CPD in a reliable manner.

In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks represent mappings from a set of inputs to a set of probability distributions over the set of outputs. In particular, even if the sets of inputs and outputs are finite, the class of stochastic mappings in question is not finite. Moreover, while for a deterministic function the values of all output variables can be computed independently of each other given the values of the inputs, in the stochastic setting the values of the output variables may need to be correlated, which requires that their values are computed jointly. A prominent class of stochastic feedforward networks which has played a key role in the resurgence of deep learning are deep belief networks. The representational power of these networks has been studied mainly in the generative setting, as models of probability distributions without an input, or in the discriminative setting for the special case of deterministic mappings. We study the representational power of deep sigmoid belief networks in terms of compositions of linear transformations of probability distributions, Markov kernels, that can be expressed by the layers of the network. We investigate different types of shallow and deep architectures, and the minimal number of layers and units per layer that are sufficient and necessary in order for the network to be able to approximate any given stochastic mapping from the set of inputs to the set of outputs arbitrarily well.

The aim of clinical effectiveness research using repositories of electronic health records is to identify what health interventions 'work best' in real-world settings. Since there are several reasons why the net benefit of intervention may differ across patients, current comparative effectiveness literature focuses on investigating heterogeneous treatment effect and predicting whether an individual might benefit from an intervention. The majority of this literature has concentrated on the estimation of the effect of treatment on binary outcomes. However, many medical interventions are evaluated in terms of their effect on future events, which are subject to loss to follow-up. In this study, we describe a framework for the estimation of heterogeneous treatment effect in terms of differences in time-to-event (survival) probabilities. We divide the problem into three phases: (1) estimation of treatment effect conditioned on unique sets of the covariate vector; (2) identification of features important for heterogeneity using an ensemble of non-parametric variable importance methods; and (3) estimation of treatment effect on the reference classes defined by the previously selected features, using one-step Targeted Maximum Likelihood Estimation. We conducted a series of simulation studies and found that this method performs well when either sample size or event rate is high enough and the number of covariates contributing to the effect heterogeneity is moderate. An application of this method to a clinical case study was conducted by estimating the effect of oral anticoagulants on newly diagnosed non-valvular atrial fibrillation patients using data from the UK Clinical Practice Research Datalink.

Markov chain Monte Carlo (MCMC) methods and neural networks are instrumental in tackling inferential and prediction problems. However, Bayesian inference based on joint use of MCMC methods and of neural networks is limited. This paper reviews the main challenges posed by neural networks to MCMC developments, including lack of parameter identifiability due to weight symmetries, prior specification effects, and consequently high computational cost and convergence failure. Population and manifold MCMC algorithms are combined to demonstrate these challenges via multilayer perceptron (MLP) examples and to develop case studies for assessing the capacity of approximate inference methods to uncover the posterior covariance of neural network parameters. Some of these challenges, such as high computational cost arising from the application of neural networks to big data and parameter identifiability arising from weight symmetries, stimulate research towards more scalable approximate MCMC methods or towards MCMC methods in reduced parameter spaces.

In the last years, Artificial Intelligence (AI) has achieved a notable momentum that may deliver the best of expectations over many application sectors across the field. For this to occur, the entire community stands in front of the barrier of explainability, an inherent problem of AI techniques brought by sub-symbolism (e.g. ensembles or Deep Neural Networks) that were not present in the last hype of AI. Paradigms underlying this problem fall within the so-called eXplainable AI (XAI) field, which is acknowledged as a crucial feature for the practical deployment of AI models. This overview examines the existing literature in the field of XAI, including a prospect toward what is yet to be reached. We summarize previous efforts to define explainability in Machine Learning, establishing a novel definition that covers prior conceptual propositions with a major focus on the audience for which explainability is sought. We then propose and discuss about a taxonomy of recent contributions related to the explainability of different Machine Learning models, including those aimed at Deep Learning methods for which a second taxonomy is built. This literature analysis serves as the background for a series of challenges faced by XAI, such as the crossroads between data fusion and explainability. Our prospects lead toward the concept of Responsible Artificial Intelligence, namely, a methodology for the large-scale implementation of AI methods in real organizations with fairness, model explainability and accountability at its core. Our ultimate goal is to provide newcomers to XAI with a reference material in order to stimulate future research advances, but also to encourage experts and professionals from other disciplines to embrace the benefits of AI in their activity sectors, without any prior bias for its lack of interpretability.

Beating humans in a penny-matching game by leveraging cognitive hierarchy theory and Bayesian learning Ran Tian, Nan Li, Ilya Kolmanovsky, and Anouck Girard Abstract -- It is a longstanding goal of artificial intelligence (AI) to be superior to human beings in decision making. Games are suitable for testing AI capabilities of making good decisions in non-numerical tasks. In this paper, we develop a new AI algorithm to play the penny-matching game considered in Shannon's "mind-reading machine" (1953) against human players. In particular, we exploit cognitive hierarchy theory and Bayesian learning techniques to continually evolve a model for predicting human player decisions, and let the AI player make decisions according to the model predictions to pursue the best chance of winning. Experimental results show that our AI algorithm beats 27 out of 30 volunteer human players. I NTRODUCTION Developing artificial intelligence (AI) to beat humans in strategic games has been drawing attention/interest of researchers for decades [1]-[10].

Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian regularizations in a specific category of DNNs, i.e., Convolutional Neural Networks (CNNs). First, we introduce a novel probabilistic representation for the hidden layers of CNNs and demonstrate that CNNs correspond to Bayesian networks with the serial connection. Furthermore, we show that the hidden layers close to the input formulate prior distributions, thus CNNs have explicitly Bayesian regularizations based on the Bayesian regularization theory. In addition, we clarify two recently observed empirical phenomena that are inconsistent with traditional theories of generalization. Finally, we validate the proposed theory on a synthetic dataset

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular. 1 Introduction Machine learning is essentially concerned with extracting models from data and using these models to make predictions.

Resting-state brain networks represent the intrinsic state of the brain during the majority of cognitive and sensorimotor tasks. However, no study has yet presented concise predictors of task-induced vigilance variability from spectrospatial features of the pre-task, resting-state electroencephalograms (EEG). We asked ten healthy volunteers (6 females, 4 males) to participate in 105-minute fixed-sequence-varying-duration sessions of sustained attention to response task (SART). A novel and adaptive vigilance scoring scheme was designed based on the performance and response time in consecutive trials, and demonstrated large inter-participant variability in terms of maintaining consistent tonic performance. Multiple linear regression using feature relevance analysis obtained significant predictors of the mean cumulative vigilance score (CVS), mean response time, and variabilities of these scores from the resting-state, band-power ratios of EEG signals, p<0.05. Single-layer neural networks trained with cross-validation also captured different associations for the beta sub-bands. Increase in the gamma (28-48 Hz) and upper beta ratios from the left central and temporal regions predicted slower reactions and more inconsistent vigilance as explained by the increased activation of default mode network (DMN) and differences between the high- and low-attention networks at temporal regions. Higher ratios of parietal alpha from the Brodmann's areas 18, 19, and 37 during the eyes-open states predicted slower responses but more consistent CVS and reactions associated with the superior ability in vigilance maintenance. The proposed framework and these findings on the most stable and significant attention predictors from the intrinsic EEG power ratios can be used to model attention variations during the calibration sessions of BCI applications and vigilance monitoring systems.