The notion of Craig interpolant, used as a form of explanation in automated reasoning, is adapted from logical inference to statistical inference and used to explain inferences made by neural networks. The method produces explanations that are at the same time concise, understandable and precise.

This paper proposes a thorough theoretical analysis of Stochastic Gradient Descent (SGD) with decreasing step sizes. First, we show that the recursion defining SGD can be provably approximated by solutions of a time inhomogeneous Stochastic Differential Equation (SDE) in a weak and strong sense. Then, motivated by recent analyses of deterministic and stochastic optimization methods by their continuous counterpart, we study the long-time convergence of the continuous processes at hand and establish non-asymptotic bounds. To that purpose, we develop new comparison techniques which we think are of independent interest. This continuous analysis allows us to develop an intuition on the convergence of SGD and, adapting the technique to the discrete setting, we show that the same results hold to the corresponding sequences. In our analysis, we notably obtain non-asymptotic bounds in the convex setting for SGD under weaker assumptions than the ones considered in previous works. Finally, we also establish finite time convergence results under various conditions, including relaxations of the famous {\L}ojasiewicz inequality, which can be applied to a class of non-convex functions.

Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. As a specific case of higher order permutation equivariant networks, we present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable. We demonstrate the efficacy of this architecture on the tasks of link prediction in citation graphs and molecular graph generation.

In a paper published on the preprint server Arxiv.org this week, IBM researchers describe SeizureNet, a machine learning framework that learns the features of seizures to classify various types. They say that it achieves state-of-the-art classification accuracy on a popular data set, and that it helps to improve the classification accuracy of smaller networks for applications with low memory and faster inference. If the claims stand up to academic scrutiny, the framework could, for instance, help the over 3.4 million people with epilepsy better understand the factors that trigger their seizures. The World Health Organization estimates that up to 70% of people living with epilepsy could live seizure-free if properly diagnosed and treated. SeizureNet is a machine learning framework consisting of individual classifiers (specifically convolutional neural networks) that learn the features of electroencephalograms (EEGs) -- i.e., tests that evaluate the electrical activity in the brain -- to predict seizure types.

We present a deep generative model of question-answer (QA) pairs for machine reading comprehension. We introduce two independent latent random variables into our model in order to diversify answers and questions separately. We also study the effect of explicitly controlling the KL term in the variational lower bound in order to avoid the "posterior collapse" issue, where the model ignores latent variables and generates QA pairs that are almost the same. Our experiments on SQuAD v1.1 showed that variational methods can aid QA pair modeling capacity, and that the controlled KL term can significantly improve diversity while generating high-quality questions and answers comparable to those of the existing systems.

High-capacity models require vast amounts of data, and data augmentation is a common remedy when this resource is limited. Standard augmentation techniques apply small hand-tuned transformations to existing data, which is a brittle process that realistically only allows for simple transformations. We propose a Bayesian interpretation of data augmentation where the transformations are modelled as latent variables to be marginalized, and show how these can be inferred variationally in an end-to-end fashion. This allows for significantly more complex transformations than manual tuning, and the marginalization implies a form of test-time data augmentation. The resulting model can be interpreted as a probabilistic extension of spatial transformer networks. Experimentally, we demonstrate improvements in accuracy and uncertainty quantification in image and time series classification tasks.

In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the proportions of labels on the distribution underlying the sample. This model of learning is applicable to a wide variety of settings, including predicting the number of votes for candidates in political elections from polls. In this paper, we formally define this class and resolve foundational questions regarding the computational complexity of LLP and characterize its relationship to PAC learning. Among our results, we show, perhaps surprisingly, that for finite VC classes what can be efficiently LLP learned is a strict subset of what can be leaned efficiently in PAC, under standard complexity assumptions. We also show that there exist classes of functions whose learnability in LLP is independent of ZFC, the standard set theoretic axioms. This implies that LLP learning cannot be easily characterized (like PAC by VC dimension).

In this work we introduce QuantNet: an architecture that is capable of transferring knowledge over systematic trading strategies in several financial markets. By having a system that is able to leverage and share knowledge across them, our aim is two-fold: to circumvent the so-called Backtest Overfitting problem; and to generate higher risk-adjusted returns and fewer drawdowns. To do that, QuantNet exploits a form of modelling called Transfer Learning, where two layers are market-specific and another one is market-agnostic. This ensures that the transfer occurs across trading strategies, with the market-agnostic layer acting as a vehicle to share knowledge, cross-influence each strategy parameters, and ultimately the trading signal produced. In order to evaluate QuantNet, we compared its performance in relation to the option of not performing transfer learning, that is, using market-specific old-fashioned machine learning. In summary, our findings suggest that QuantNet performs better than non transfer-based trading strategies, improving Sharpe ratio in 15% and Calmar ratio in 41% across 3103 assets in 58 equity markets across the world. Code coming soon.

The mixture extension of exponential family principal component analysis (EPCA) was designed to encode much more structural information about data distribution than the traditional EPCA does. For example, due to the linearity of EPCA's essential form, nonlinear cluster structures cannot be easily handled, but they are explicitly modeled by the mixing extensions. However, the traditional mixture of local EPCAs has the problem of model redundancy, i.e., overlaps among mixing components, which may cause ambiguity for data clustering. To alleviate this problem, in this paper, a repulsiveness-encouraging prior is introduced among mixing components and a diversified EPCA mixture (DEPCAM) model is developed in the Bayesian framework. Specifically, a determinantal point process (DPP) is exploited as a diversity-encouraging prior distribution over the joint local EPCAs. As required, a matrix-valued measure for L-ensemble kernel is designed, within which, $\ell_1$ constraints are imposed to facilitate selecting effective PCs of local EPCAs, and angular based similarity measure are proposed. An efficient variational EM algorithm is derived to perform parameter learning and hidden variable inference. Experimental results on both synthetic and real-world datasets confirm the effectiveness of the proposed method in terms of model parsimony and generalization ability on unseen test data.

Inability to test at scale has become Achille's heel in humanity's ongoing war against COVID-19 pandemic. An agile, scalable and cost-effective testing, deployable at a global scale, can act as a game changer in this war. To address this challenge, building on the promising results of our prior work on cough-based diagnosis of a motley of respiratory diseases, we develop an Artificial Intelligence (AI)-based test for COVID-19 preliminary diagnosis. The test is deployable at scale through a mobile app named AI4COVID-19. The AI4COVID-19 app requires 2-second cough recordings of the subject. By analyzing the cough samples through an AI engine running in the cloud, the app returns a preliminary diagnosis within a minute. Unfortunately, cough is common symptom of over two dozen non-COVID-19 related medical conditions. This makes the COVID-19 diagnosis from cough alone an extremely challenging problem. We solve this problem by developing a novel multi-pronged mediator centered risk-averse AI architecture that minimizes misdiagnosis. At the time of writing, our AI engine can distinguish between COVID-19 patient coughs and several types of non-COVID-19 coughs with over 90% accuracy. AI4COVID-19's performance is likely to improve as more and better data becomes available. This paper presents a proof of concept to encourage controlled clinical trials and serves as a call for labeled cough data. AI4COVID-19 is not designed to compete with clinical testing. Instead, it offers a complementing tele-testing tool deployable anytime, anywhere, by anyone, so clinical-testing and treatment can be channeled to those who need it the most, thereby saving more lives.