Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function estimators that makes use of double control variates. These control variates act on top of a main control variate, and try to further reduce the variance of the overall estimator. We develop a double control variate for the REINFORCE leave-one-out estimator using Taylor expansions. For training discrete latent variable models, such as variational autoencoders with binary latent variables, our approach adds no extra computational cost compared to standard training with the REINFORCE leave-one-out estimator. We apply our method to challenging high-dimensional toy examples and training variational autoencoders with binary latent variables. We show that our estimator can have lower variance compared to other state-of-the-art estimators.

Artificial intelligence (AI) systems have become increasingly popular in many areas. Nevertheless, AI technologies are still in their developing stages, and many issues need to be addressed. Among those, the reliability of AI systems needs to be demonstrated so that the AI systems can be used with confidence by the general public. In this paper, we provide statistical perspectives on the reliability of AI systems. Different from other considerations, the reliability of AI systems focuses on the time dimension. That is, the system can perform its designed functionality for the intended period. We introduce a so-called SMART statistical framework for AI reliability research, which includes five components: Structure of the system, Metrics of reliability, Analysis of failure causes, Reliability assessment, and Test planning. We review traditional methods in reliability data analysis and software reliability, and discuss how those existing methods can be transformed for reliability modeling and assessment of AI systems. We also describe recent developments in modeling and analysis of AI reliability and outline statistical research challenges in this area, including out-of-distribution detection, the effect of the training set, adversarial attacks, model accuracy, and uncertainty quantification, and discuss how those topics can be related to AI reliability, with illustrative examples. Finally, we discuss data collection and test planning for AI reliability assessment and how to improve system designs for higher AI reliability. The paper closes with some concluding remarks.

Markov decision processes are typically used for sequential decision making under uncertainty. For many aspects however, ranging from constrained or safe specifications to various kinds of temporal (non-Markovian) dependencies in task and reward structures, extensions are needed. To that end, in recent years interest has grown into combinations of reinforcement learning and temporal logic, that is, combinations of flexible behavior learning methods with robust verification and guarantees. In this paper we describe an experimental investigation of the recently introduced regular decision processes that support both non-Markovian reward functions as well as transition functions. In particular, we provide a tool chain for regular decision processes, algorithmic extensions relating to online, incremental learning, an empirical evaluation of model-free and model-based solution algorithms, and applications in regular, but non-Markovian, grid worlds.

We derive information-theoretic lower bounds on the Bayes risk and generalization error of realizable machine learning models. In particular, we employ an analysis in which the rate-distortion function of the model parameters bounds the required mutual information between the training samples and the model parameters in order to learn a model up to a Bayes risk constraint. For realizable models, we show that both the rate distortion function and mutual information admit expressions that are convenient for analysis. For models that are (roughly) lower Lipschitz in their parameters, we bound the rate distortion function from below, whereas for VC classes, the mutual information is bounded above by $d_\mathrm{vc}\log(n)$. When these conditions match, the Bayes risk with respect to the zero-one loss scales no faster than $\Omega(d_\mathrm{vc}/n)$, which matches known outer bounds and minimax lower bounds up to logarithmic factors. We also consider the impact of label noise, providing lower bounds when training and/or test samples are corrupted.

To explain the decision of any model, we extend the notion of probabilistic Sufficient Explanations (P-SE). For each instance, this approach selects the minimal subset of features that is sufficient to yield the same prediction with high probability, while removing other features. The crux of P-SE is to compute the conditional probability of maintaining the same prediction. Therefore, we introduce an accurate and fast estimator of this probability via random Forests for any data $(\boldsymbol{X}, Y)$ and show its efficiency through a theoretical analysis of its consistency. As a consequence, we extend the P-SE to regression problems. In addition, we deal with non-binary features, without learning the distribution of $X$ nor having the model for making predictions. Finally, we introduce local rule-based explanations for regression/classification based on the P-SE and compare our approaches w.r.t other explainable AI methods. These methods are publicly available as a Python package at \url{www.github.com/salimamoukou/acv00}.

Most existing classification methods aim to minimize the overall misclassification error rate, however, in applications, different types of errors can have different consequences. To take into account this asymmetry issue, two popular paradigms have been developed, namely the Neyman-Pearson (NP) paradigm and cost-sensitive (CS) paradigm. Compared to CS paradigm, NP paradigm does not require a specification of costs. Most previous works on NP paradigm focused on the binary case. In this work, we study the multi-class NP problem by connecting it to the CS problem, and propose two algorithms. We extend the NP oracle inequalities and consistency from the binary case to the multi-class case, and show that our two algorithms enjoy these properties under certain conditions. The simulation and real data studies demonstrate the effectiveness of our algorithms. To our knowledge, this is the first work to solve the multi-class NP problem via cost-sensitive learning techniques with theoretical guarantees. The proposed algorithms are implemented in the R package "npcs" on CRAN.

Data on high-dimensional spheres arise frequently in many disciplines either naturally or as a consequence of preliminary processing and can have intricate dependence structure that needs to be understood. We develop exploratory factor analysis of the projected normal distribution to explain the variability in such data using a few easily interpreted latent factors. Our methodology provides maximum likelihood estimates through a novel fast alternating expectation profile conditional maximization algorithm. Results on simulation experiments on a wide range of settings are uniformly excellent. Our methodology provides interpretable and insightful results when applied to tweets with the $\#MeToo$ hashtag in early December 2018, to time-course functional Magnetic Resonance Images of the average pre-teen brain at rest, to characterize handwritten digits, and to gene expression data from cancerous cells in the Cancer Genome Atlas.

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of `automatic relevance determination' kernels, but in high-dimensional datasets this approach can be unreliable. A more probabilistically principled alternative is to use spike and slab priors and infer a posterior probability of variable inclusion. However, existing implementations in GPs are extremely costly to run in both high-dimensional and large-$n$ datasets, or are intractable for most kernels. As such, we develop a fast and scalable variational inference algorithm for the spike and slab GP that is tractable with arbitrary differentiable kernels. We improve our algorithm's ability to adapt to the sparsity of relevant variables by Bayesian model averaging over hyperparameters, and achieve substantial speed ups using zero temperature posterior restrictions, dropout pruning and nearest neighbour minibatching. In experiments our method consistently outperforms vanilla and sparse variational GPs whilst retaining similar runtimes (even when $n=10^6$) and performs competitively with a spike and slab GP using MCMC but runs up to $1000$ times faster.

Unsupervised dialogue structure learning is an important and meaningful task in natural language processing. The extracted dialogue structure and process can help analyze human dialogue, and play a vital role in the design and evaluation of dialogue systems. The traditional dialogue system requires experts to manually design the dialogue structure, which is very costly. But through unsupervised dialogue structure learning, dialogue structure can be automatically obtained, reducing the cost of developers constructing dialogue process. The learned dialogue structure can be used to promote the dialogue generation of the downstream task system, and improve the logic and consistency of the dialogue robot's reply.In this paper, we propose a Bert-based unsupervised dialogue structure learning algorithm DSBERT (Dialogue Structure BERT). Different from the previous SOTA models VRNN and SVRNN, we combine BERT and AutoEncoder, which can effectively combine context information. In order to better prevent the model from falling into the local optimal solution and make the dialogue state distribution more uniform and reasonable, we also propose three balanced loss functions that can be used for dialogue structure learning. Experimental results show that DSBERT can generate a dialogue structure closer to the real structure, can distinguish sentences with different semantics and map them to different hidden states.

Reconstructing missing information in epidemic spreading on contact networks can be essential in prevention and containment strategies. For instance, identifying and warning infective but asymptomatic individuals (e.g., manual contact tracing) helped contain outbreaks in the COVID-19 pandemic. The number of possible epidemic cascades typically grows exponentially with the number of individuals involved. The challenge posed by inference problems in the epidemics processes originates from the difficulty of identifying the almost negligible subset of those compatible with the evidence (for instance, medical tests). Here we present a new generative neural networks framework that can sample the most probable infection cascades compatible with observations. Moreover, the framework can infer the parameters governing the spreading of infections. The proposed method obtains better or comparable results with existing methods on the patient zero problem, risk assessment, and inference of infectious parameters in synthetic and real case scenarios like spreading infections in workplaces and hospitals.