Networks of spiking neurons and Winner-Take-All spiking circuits (WTA-SNNs) can detect information encoded in spatio-temporal multi-valued events. These are described by the timing of events of interest, e.g., clicks, as well as by categorical numerical values assigned to each event, e.g., like or dislike. Other use cases include object recognition from data collected by neuromorphic cameras, which produce, for each pixel, signed bits at the times of sufficiently large brightness variations. Existing schemes for training WTA-SNNs are limited to rate-encoding solutions, and are hence able to detect only spatial patterns. Developing more general training algorithms for arbitrary WTA-SNNs inherits the challenges of training (binary) Spiking Neural Networks (SNNs). These amount, most notably, to the non-differentiability of threshold functions, to the recurrent behavior of spiking neural models, and to the difficulty of implementing backpropagation in neuromorphic hardware. In this paper, we develop a variational online local training rule for WTA-SNNs, referred to as VOWEL, that leverages only local pre- and post-synaptic information for visible circuits, and an additional common reward signal for hidden circuits. The method is based on probabilistic generalized linear neural models, control variates, and variational regularization. Experimental results on real-world neuromorphic datasets with multi-valued events demonstrate the advantages of WTA-SNNs over conventional binary SNNs trained with state-of-the-art methods, especially in the presence of limited computing resources.

We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems.

Over this decade, an increasing number of processes is being automated through classification algorithms, being essential that these are robust and reliable if we are to trust key operations based on their output. State-of-the-art classifiers perform extraordinarily well on standard data, but they have been shown to be vulnerable to adversarial examples, data instances specifically targeted at fooling the algorithms (Comiter, 2019). As a fundamental hypothesis, algorithms rely on the use of independent and identically distributed (iid) data for both the training and test phases. However, security aspects in classification, which form part of the field of adversarial machine learning (AML), question such hypothesis due to the presence of adversaries ready to modify the data to obtain a benefit and, thus, making both distributions differ. Stemming from the pioneering work in adversarial classification (AC) in Dalvi et al. (2004), the paradigm used to model the confrontation between adversaries and classification systems has been game theory, see recent reviews in Biggio and Roli (2018) and Zhou et al. (2018). As an example, the most popular attacks, including the fast gradient sign method (FGSM) (Goodfellow et al., 2014b), may be viewed from a game-theoretic perspective. Similarly, two of the most promising defence techniques, adversarial training (AT) (Madry et al., 2018), which trains the defender model with attacked samples, and adversarial logit pairing (ALP) (Kannan et al., 2018), which encourages the logits of the model to be the same for both standard and adversarial inputs, may be framed in game theoretic terms. This perspective typically entails common knowledge hypothesis (Hargreaves-Heap and Varoufakis, 2004) which, from a fundamental point of view, are not sustainable in settings such as security, as adversaries try to hide and conceal information. Recent work (Naveiro et al., 2019) presented ACRA, a novel approach for AC based on Adversarial Risk

Biomedical data is filled with continuous real values; these values in the feature set tend to create problems like underfitting, the curse of dimensionality and increase in misclassification rate because of higher variance. In response, pre-processing techniques on dataset minimizes the side effects and have shown success in maintaining the adequate accuracy. Feature selection and discretization are the two necessary preprocessing steps that were effectively employed to handle the data redundancies in the biomedical data. However, in the previous works, the absence of unified effort by integrating feature selection and discretization together in solving the data redundancy problem leads to the disjoint and fragmented field. This paper proposes a novel multi-objective based dimensionality reduction framework, which incorporates both discretization and feature reduction as an ensemble model for performing feature selection and discretization. Selection of optimal features and the categorization of discretized and non-discretized features from the feature subset is governed by the multi-objective genetic algorithm (NSGA-II). The two objective, minimizing the error rate during the feature selection and maximizing the information gain while discretization is considered as fitness criteria.

Autonomous vehicles must be comprehensively evaluated before deployed in cities and highways. Current evaluation procedures lack the abilities of weakness-aiming and evolving, thus they could hardly generate adversarial environments for autonomous vehicles, leading to insufficient challenges. To overcome the shortage of static evaluation methods, this paper proposes a novel method to generate adversarial environments with deep reinforcement learning, and to cluster them with a nonparametric Bayesian method. As a representative task of autonomous driving, lane-change is used to demonstrate the superiority of the proposed method. First, two lane-change models are separately developed by a rule-based method and a learning-based method, waiting for evaluation and comparison. Next, adversarial environments are generated by training surrounding interactive vehicles with deep reinforcement learning for local optimal ensembles. Then, a nonparametric Bayesian approach is utilized to cluster the adversarial policies of the interactive vehicles. Finally, the adversarial environment patterns are illustrated and the performances of two lane-change models are evaluated and compared. The simulation results indicate that both models perform significantly worse in adversarial environments than in naturalistic environments, with plenty of weaknesses successfully extracted in a few tests.

In the past twenty years there has been an explosion of the use of graphical models to represent the relationship between a vector of random variables and perform distributed inference which takes advantage of the underlying graphical representations. Bayesian networks (BNs) (Darwiche 2009; Fenton and Neil 2012) are nowadays the most used graphical models, with applications to a wide array of domains and implementation in various software: for instance, the R packages bnlearn by Scutari (2010) and gRain by Højsgaard (2012), among others. However, BNs can only represent symmetric conditional independences which in practical applications may not be fully justified. For this reason, a variety of models that can take into account the asymmetric nature of real-world data have been proposed; for example, context-specific BNs (Boutilier, Friedman, Goldszmidt, and Koller 1996), labeled directed acyclic graphs (Pensar, Nyman, Koski, and Corander 2015) and probabilistic decision graphs (Jaeger, Nielsen, and Silander 2006). Unlike most of its competitors, the chain event graph (CEG) (Collazo, Görgen, and Smith 2018; Smith and Anderson 2008; Riccomagno and Smith 2004, 2009) can capture all (context-specific) conditional independences in a unique graph, obtained by a coalescence over the vertices of an appropriately constructed probability tree, called staged tree.

We study the problem of learning from aggregate observations where supervision signals are given to sets of instances instead of individual instances, while the goal is still to predict labels of unseen individuals. A well-known example is multiple instance learning (MIL). In this paper, we extend MIL beyond binary classification to other problems such as multiclass classification and regression. We present a probabilistic framework that is applicable to a variety of aggregate observations, e.g., pairwise similarity for classification and mean/difference/rank observation for regression. We propose a simple yet effective method based on the maximum likelihood principle, which can be simply implemented for various differentiable models such as deep neural networks and gradient boosting machines. Experiments on three novel problem settings -- classification via triplet comparison and regression via mean/rank observation indicate the effectiveness of the proposed method.

We consider the situation where the observed sample contains some observations whose class of origin is known (that is, they are classified with respect to the g underlying classes of interest), and where the remaining observations in the sample are unclassified (that is, their class labels are unknown). For class-conditional distributions taken to be known up to a vector of unknown parameters, the aim is to estimate the Bayes' rule of allocation for the allocation of subsequent unclassified observations. Estimation on the basis of both the classified and unclassified data can be undertaken in a straightforward manner by fitting a g-component mixture model by maximum likelihood (ML) via the EM algorithm in the situation where the observed data can be assumed to be an observed random sample from the adopted mixture distribution. This assumption applies if the missing-data mechanism is ignorable in the terminology pioneered by Rubin (1976). An initial likelihood approach was to use the so-called classification ML approach whereby the missing labels are taken to be parameters to be estimated along with the parameters of the class-conditional distributions. However, as it can lead to inconsistent estimates, the focus of attention switched to the mixture ML approach after the appearance of the EM algorithm (Dempster et al., 1977). Particular attention is given here to the asymptotic relative efficiency (ARE) of the Bayes' rule estimated from a partially classified sample. Lastly, we consider briefly some recent results in situations where the missing label pattern is non-ignorable for the purposes of ML estimation for the mixture model.

Probabilistic circuits (PCs) are a promising avenue for probabilistic modeling, as they permit a wide range of exact and efficient inference routines. Recent ``deep-learning-style'' implementations of PCs strive for a better scalability, but are still difficult to train on real-world data, due to their sparsely connected computational graphs. In this paper, we propose Einsum Networks (EiNets), a novel implementation design for PCs, improving prior art in several regards. At their core, EiNets combine a large number of arithmetic operations in a single monolithic einsum-operation, leading to speedups and memory savings of up to two orders of magnitude, in comparison to previous implementations. As an algorithmic contribution, we show that the implementation of Expectation-Maximization (EM) can be simplified for PCs, by leveraging automatic differentiation. Furthermore, we demonstrate that EiNets scale well to datasets which were previously out of reach, such as SVHN and CelebA, and that they can be used as faithful generative image models.

The process of discovery in the physical, biological and medical sciences can be painstakingly slow. Most experiments fail, and the time from initiation of research until a new advance reaches commercial production can span 20 years. This tutorial is aimed to provide experimental scientists with a foundation in the science of making decisions. Using numerical examples drawn from the experiences of the authors, the article describes the fundamental elements of any experimental learning problem. It emphasizes the important role of belief models, which include not only the best estimate of relationships provided by prior research, previous experiments and scientific expertise, but also the uncertainty in these relationships. We introduce the concept of a learning policy, and review the major categories of policies. We then introduce a policy, known as the knowledge gradient, that maximizes the value of information from each experiment. We bring out the importance of reducing uncertainty, and illustrate this process for different belief models.