Most topic models are constructed under the assumption that documents follow a multinomial distribution. The Poisson distribution is an alternative distribution to describe the probability of count data. For topic modelling, the Poisson distribution describes the number of occurrences of a word in documents of fixed length. The Poisson distribution has been successfully applied in text classification, but its application to topic modelling is not well documented, specifically in the context of a generative probabilistic model. Furthermore, the few Poisson topic models in literature are admixture models, making the assumption that a document is generated from a mixture of topics. In this study, we focus on short text. Many studies have shown that the simpler assumption of a mixture model fits short text better. With mixture models, as opposed to admixture models, the generative assumption is that a document is generated from a single topic. One topic model, which makes this one-topic-per-document assumption, is the Dirichlet-multinomial mixture model. The main contributions of this work are a new Gamma-Poisson mixture model, as well as a collapsed Gibbs sampler for the model. The benefit of the collapsed Gibbs sampler derivation is that the model is able to automatically select the number of topics contained in the corpus. The results show that the Gamma-Poisson mixture model performs better than the Dirichlet-multinomial mixture model at selecting the number of topics in labelled corpora. Furthermore, the Gamma-Poisson mixture produces better topic coherence scores than the Dirichlet-multinomial mixture model, thus making it a viable option for the challenging task of topic modelling of short text.

A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learning (SRL) frameworks, these models are not projective in the sense that the marginal of the distribution for size-$n$ structures on induced sub-structures of size $k

Some challenging problems in tracking multiple objects include the time-dependent cardinality, unordered measurements and object parameter labeling. In this paper, we employ Bayesian Bayesian nonparametric methods to address these challenges. In particular, we propose modeling the multiple object parameter state prior using the dependent Dirichlet and Pitman-Yor processes. These nonparametric models have been shown to be more flexible and robust, when compared to existing methods, for estimating the time-varying number of objects, providing object labeling and identifying measurement to object associations. Monte Carlo sampling methods are then proposed to efficiently learn the trajectory of objects from noisy measurements. Using simulations, we demonstrate the estimation performance advantage of the new methods when compared to existing algorithms such as the generalized labeled multi-Bernoulli filter.

Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal DAGs with non-Gaussian and/or nonlinear structural equation models (SEMs). In this paper, we focus on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, and propose a novel test for non-invertible bivariate causal models. We further develop a method to incorporate this test in structure learning of DAGs that contain both linear and nonlinear causal relations. By extensive numerical comparisons, we show that our algorithms outperform existing DAG learning methods in identifying causal graphical structures. We illustrate the practical application of our method in learning causal networks for combinatorial binding of transcription factors from ChIP-Seq data.

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 study minimax convergence rates of nonparametric density estimation in the Huber contamination model, in which a proportion of the data comes from an unknown outlier distribution. We provide the first results for this problem under a large family of losses, called Besov integral probability metrics (IPMs), that includes $\mathcal{L}^p$, Wasserstein, Kolmogorov-Smirnov, and other common distances between probability distributions. Specifically, under a range of smoothness assumptions on the population and outlier distributions, we show that a re-scaled thresholding wavelet series estimator achieves minimax optimal convergence rates under a wide variety of losses. Finally, based on connections that have recently been shown between nonparametric density estimation under IPM losses and generative adversarial networks (GANs), we show that certain GAN architectures also achieve these minimax rates.

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

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric Bayesian inference-based uncertainty propagation approach, called Gaussian Process (GP). We also suggest a new type of sensitivity called Subspace-wise Sensitivity, using observations on the interpretability of GP-POPF hyperparameters. The simulation results on 14-bus and 30-bus systems show that the proposed method provides reasonably accurate solutions when compared with Monte-Carlo Simulations (MCS) solutions at different levels of uncertain renewable penetration as well as load uncertainties, while requiring much less number of samples and elapsed time.

Learning disabilities like dysgraphia, dyslexia, dyspraxia, etc. interfere with academic achievements but have also long terms consequences beyond the academic time. It is widely admitted that between 5% to 10% of the world population is subject to this kind of disabilities. For assessing such disabilities in early childhood, children have to solve a battery of tests. Human experts score these tests, and decide whether the children require specific education strategy on the basis of their marks. The assessment can be lengthy, costly and emotionally painful. In this paper, we investigate how Artificial Intelligence can help in automating this assessment. Gathering a dataset of handwritten text pictures and audio recordings, both from standard children and from dyslexic and/or dysgraphic children, we apply machine learning techniques for classification in order to analyze the differences between dyslexic/dysgraphic and standard readers/writers and to build a model. The model is trained on simple features obtained by analysing the pictures and the audio files. Our preliminary implementation shows relatively high performances on the dataset we have used. This suggests the possibility to screen dyslexia and dysgraphia via non-invasive methods in an accurate way as soon as enough data are available.