Bilevel optimization (BLO) is a popular approach with many applications including hyperparameter optimization, neural architecture search, adversarial robustness and model-agnostic meta-learning. However, the approach suffers from time and memory complexity proportional to the length $r$ of its inner optimization loop, which has led to several modifications being proposed. One such modification is \textit{first-order} BLO (FO-BLO) which approximates outer-level gradients by zeroing out second derivative terms, yielding significant speed gains and requiring only constant memory as $r$ varies. Despite FO-BLO's popularity, there is a lack of theoretical understanding of its convergence properties. We make progress by demonstrating a rich family of examples where FO-BLO-based stochastic optimization does not converge to a stationary point of the BLO objective. We address this concern by proposing a new FO-BLO-based unbiased estimate of outer-level gradients, enabling us to theoretically guarantee this convergence, with no harm to memory and expected time complexity. Our findings are supported by experimental results on Omniglot and Mini-ImageNet, popular few-shot meta-learning benchmarks.

We propose a novel GAN framework for non-parametric density estimation with high-dimensional data. This framework is based on a novel density estimator, called the hyperbolic cross density estimator, which enjoys nice convergence properties in the mixed Sobolev spaces. As modifications of the usual Sobolev spaces, the mixed Sobolev spaces are more suitable for describing high-dimensional density functions. We prove that, unlike other existing approaches, the proposed GAN framework does not suffer the curse of dimensionality and can achieve the optimal convergence rate of $O_p(n^{-1/2})$, with $n$ data points in an arbitrary fixed dimension. We also study the universality of GANs in terms of the existence of ReLU networks which can approximate the density functions in the mixed Sobolev spaces up to any accuracy level.

The explosion of disinformation related to the COVID-19 pandemic has overloaded fact-checkers and media worldwide. To help tackle this, we developed computational methods to support COVID-19 disinformation debunking and social impacts research. This paper presents: 1) the currently largest available manually annotated COVID-19 disinformation category dataset; and 2) a classification-aware neural topic model (CANTM) that combines classification and topic modelling under a variational autoencoder framework. We demonstrate that CANTM efficiently improves classification performance with low resources, and is scalable. In addition, the classification-aware topics help researchers and end-users to better understand the classification results.

Entropy augmented to reward is known to soften the greedy argmax policy to softmax policy. Entropy augmentation is reformulated and leads to a motivation to introduce an additional entropy term to the objective function in the form of KL-divergence to regularize optimization process. It results in a policy which monotonically improves while interpolating from the current policy to the softmax greedy policy. This policy is used to build a continuously parameterized algorithm which optimize policy and Q-function simultaneously and whose extreme limits correspond to policy gradient and Q-learning, respectively. Experiments show that there can be a performance gain using an intermediate algorithm. Both Q-learning[15] and policy gradient(PG)[13] update policy towards greedy one whether the policy is explicit or not.

Middle-term horizon (months to a year) power consumption prediction is a main challenge in the energy sector, in particular when probabilistic forecasting is considered. We propose a new modelling approach that incorporates trend, seasonality and weather conditions, as explicative variables in a shallow Neural Network with an autoregressive feature. We obtain excellent results for density forecast on the one-year test set applying it to the daily power consumption in New England U.S.A.. The quality of the achieved power consumption probabilistic forecasting has been verified, on the one hand, comparing the results to other standard models for density forecasting and, on the other hand, considering measures that are frequently used in the energy sector as pinball loss and CI backtesting.

Several custom web scrapers were created for retrieving news articles from various online news organizations. All web scrapers were run every two hours to retrieve articles from the following five news sites: the Atlantic, the British Broadcasting Corporation (BBC) News, Fox News, the New York Times and Slate Magazine. Web scrapers continue to run every two hours in perpetuity, scraping additional news articles. Collectively, the web scrapers used each news organization's RSS feed as input, storing the scraped output into a custom database. Article URLs were used for disambiguation; where two scraped articles shared a URL, the most recently retrieved article replaced previous versions of articles. As of November 2019, we collected a total of 105,000 news articles from five media organizations. Figure 2 depicts the number of cumulative articles scraped for each news organization over time. Even though articles from Fox News were regularly scraped four months later than other news sources, the number of articles scraped rose quickly, and now constitutes the news organization with the most scraped articles. Given the news scrapers run at regularly scheduled two-hour intervals for all news organization, this suggests that Fox News updates its RSS feed with new articles far more often than others, and the Atlantic updates its RSS feed far less frequently than others.

Electronic Health Records (EHRs) are commonly used by the machine learning community for research on problems specifically related to health care and medicine. EHRs have the advantages that they can be easily distributed and contain many features useful for e.g. classification problems. What makes EHR data sets different from typical machine learning data sets is that they are often very sparse, due to their high dimensionality, and often contain heterogeneous (mixed) data types. Furthermore, the data sets deal with sensitive information, which limits the distribution of any models learned using them, due to privacy concerns. For these reasons, using EHR data in practice presents a real challenge. In this work, we explore using Generative Adversarial Networks to generate synthetic, heterogeneous EHRs with the goal of using these synthetic records in place of existing data sets for downstream classification tasks. We will further explore applying differential privacy (DP) preserving optimization in order to produce DP synthetic EHR data sets, which provide rigorous privacy guarantees, and are therefore shareable and usable in the real world. The performance (measured by AUROC, AUPRC and accuracy) of our model's synthetic, heterogeneous data is very close to the original data set (within 3 - 5% of the baseline) for the non-DP model when tested in a binary classification task. Using strong $(1, 10^{-5})$ DP, our model still produces data useful for machine learning tasks, albeit incurring a roughly 17% performance penalty in our tested classification task. We additionally perform a sub-population analysis and find that our model does not introduce any bias into the synthetic EHR data compared to the baseline in either male/female populations, or the 0-18, 19-50 and 51+ age groups in terms of classification performance for either the non-DP or DP variant.

Gaussian distributions are plentiful in applications dealing in uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries for probability measures, as the resulting geometry on Gaussians is often expressible in closed-form under the frameworks. In this work, we study the Gaussian geometry under the entropy-regularized 2-Wasserstein distance, by providing closed-form solutions for the distance and interpolations between elements. Furthermore, we provide a fixed-point characterization of a population barycenter when restricted to the manifold of Gaussians, which allows computations through the fixed-point iteration algorithm. As a consequence, the results yield closed-form expressions for the 2-Sinkhorn divergence. As the geometries change by varying the regularization magnitude, we study the limiting cases of vanishing and infinite magnitudes, reconfirming well-known results on the limits of the Sinkhorn divergence. Finally, we illustrate the resulting geometries with a numerical study.

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems involved in applying deep learning: most deep learning methods require the solution of hard optimisation problems, and a good understanding of the tradeoff between computational effort, amount of data and model complexity is required to successfully design a deep learning approach for a given problem. A large amount of progress made in deep learning has been based on heuristic explorations, but there is a growing effort to mathematically understand the structure in existing deep learning methods and to systematically design new deep learning methods to preserve certain types of structure in deep learning. In this article, we review a number of these directions: some deep neural networks can be understood as discretisations of dynamical systems, neural networks can be designed to have desirable properties such as invertibility or group equivariance, and new algorithmic frameworks based on conformal Hamiltonian systems and Riemannian manifolds to solve the optimisation problems have been proposed. We conclude our review of each of these topics by discussing some open problems that we consider to be interesting directions for future research.

Neural architecture search (NAS) has advanced significantly in recent years but most NAS systems restrict search to learning architectures of a recurrent or convolutional cell. In this paper, we extend the search space of NAS. In particular, we present a general approach to learn both intra-cell and inter-cell architectures (call it ESS). For a better search result, we design a joint learning method to perform intra-cell and inter-cell NAS simultaneously. We implement our model in a differentiable architecture search system. For recurrent neural language modeling, it outperforms a strong baseline significantly on the PTB and WikiText data, with a new state-of-the-art on PTB. Moreover, the learned architectures show good transferability to other systems. E.g., they improve state-of-the-art systems on the CoNLL and WNUT named entity recognition (NER) tasks and CoNLL chunking task, indicating a promising line of research on large-scale pre-learned architectures.