Choosing a proper set of kernel functions is an important problem in learning Gaussian Process (GP) models since each kernel structure has different model complexity and data fitness. Recently, automatic kernel composition methods provide not only accurate prediction but also attractive interpretability through search-based methods. However, existing methods suffer from slow kernel composition learning. To tackle large-scaled data, we propose a new sparse approximate posterior for GPs, MultiSVGP, constructed from groups of inducing points associated with individual additive kernels in compositional kernels. We demonstrate that this approximation provides a better fit to learn compositional kernels given empirical observations. We also theoretically justification on error bound when compared to the traditional sparse GP. In contrast to the search-based approach, we present a novel probabilistic algorithm to learn a kernel composition by handling the sparsity in the kernel selection with Horseshoe prior. We demonstrate that our model can capture characteristics of time series with significant reductions in computational time and have competitive regression performance on real-world data sets.

We propose a Distributional Approach to address Controlled Text Generation from pre-trained Language Models (LMs). This view permits to define, in a single formal framework, "pointwise" and "distributional" constraints over the target LM -- to our knowledge, this is the first approach with such generality -- while minimizing KL divergence with the initial LM distribution. The optimal target distribution is then uniquely determined as an explicit EBM (Energy-Based Model) representation. From that optimal representation we then train the target controlled autoregressive LM through an adaptive distributional variant of Policy Gradient. We conduct a first set of experiments over pointwise constraints showing the advantages of our approach over a set of baselines, in terms of obtaining a controlled LM balancing constraint satisfaction with divergence from the initial LM (GPT-2). We then perform experiments over distributional constraints, a unique feature of our approach, demonstrating its potential as a remedy to the problem of Bias in Language Models. Through an ablation study we show the effectiveness of our adaptive technique for obtaining faster convergence.

Deep Reinforcement Learning (DRL) reaches a superhuman level of play in many complete information games. The state of the art search algorithm used in combination with DRL is Monte Carlo Tree Search (MCTS). We take another approach to DRL using a Minimax algorithm instead of MCTS and learning only the evaluation of states, not the policy. We show that for multiple games it is competitive with the state of the art DRL for the learning performances and for the confrontations.

This study introduces the Territory Design for Dynamic Multi-Period Vehicle Routing Problem with Time Windows (TD-DMPVRPTW), motivated by a real-world application at a food company's distribution center. This problem deals with the design of contiguous and compact territories for delivery of orders from a depot to a set of customers, with time windows, over a multi-period planning horizon. Customers and their demands vary dynamically over time. The problem is modeled as a mixed-integer linear program (MILP) and solved by a proposed heuristic. The heuristic solutions are compared with the proposed MILP solutions on a set of small artificial instances and the food company's solutions on a set of real-world instances. Computational results show that the proposed algorithm can yield high-quality solutions within moderate running times.

Small business classification is a difficult and important task within many applications, including customer segmentation. Training on small business names introduces gender and geographic origin biases. A model for predicting one of 66 business types based only upon the business name was developed in this work (top-1 f1-score = 60.2%). Two approaches to removing the bias from this model are explored: replacing given names with a placeholder token, and augmenting the training data with gender-swapped examples. The results for these approaches is reported, and the bias in the model was reduced by hiding given names from the model. However, bias reduction was accomplished at the expense of classification performance (top-1 f1-score = 56.6%). Augmentation of the training data with gender-swapping samples proved less effective at bias reduction than the name hiding approach on the evaluated dataset.

Investors try to predict returns of financial assets to make successful investment. Many quantitative analysts have used machine learning-based methods to find unknown profitable market rules from large amounts of market data. However, there are several challenges in financial markets hindering practical applications of machine learning-based models. First, in financial markets, there is no single model that can consistently make accurate prediction because traders in markets quickly adapt to newly available information. Instead, there are a number of ephemeral and partially correct models called "alpha factors". Second, since financial markets are highly uncertain, ensuring interpretability of prediction models is quite important to make reliable trading strategies. To overcome these challenges, we propose the Trader-Company method, a novel evolutionary model that mimics the roles of a financial institute and traders belonging to it. Our method predicts future stock returns by aggregating suggestions from multiple weak learners called Traders. A Trader holds a collection of simple mathematical formulae, each of which represents a candidate of an alpha factor and would be interpretable for real-world investors. The aggregation algorithm, called a Company, maintains multiple Traders. By randomly generating new Traders and retraining them, Companies can efficiently find financially meaningful formulae whilst avoiding overfitting to a transient state of the market. We show the effectiveness of our method by conducting experiments on real market data.

Increased availability of epidemiological data, novel digital data streams, and the rise of powerful machine learning approaches have generated a surge of research activity on real-time epidemic forecast systems. In this paper, we propose the use of a novel data source, namely retail market data to improve seasonal influenza forecasting. Specifically, we consider supermarket retail data as a proxy signal for influenza, through the identification of sentinel baskets, i.e., products bought together by a population of selected customers. We develop a nowcasting and forecasting framework that provides estimates for influenza incidence in Italy up to 4 weeks ahead. We make use of the Support Vector Regression (SVR) model to produce the predictions of seasonal flu incidence. Our predictions outperform both a baseline autoregressive model and a second baseline based on product purchases. The results show quantitatively the value of incorporating retail market data in forecasting models, acting as a proxy that can be used for the real-time analysis of epidemics.

Estimating causal effects from randomized experiments is central to clinical research. Reducing the statistical uncertainty in these analyses is an important objective for statisticians. Registries, prior trials, and health records constitute a growing compendium of historical data on patients under standard-of-care conditions that may be exploitable to this end. However, most methods for historical borrowing achieve reductions in variance by sacrificing strict type-I error rate control. Here, we propose a use of historical data that exploits linear covariate adjustment to improve the efficiency of trial analyses without incurring bias. Specifically, we train a prognostic model on the historical data, then estimate the treatment effect using a linear regression while adjusting for the trial subjects' predicted outcomes (their prognostic scores). We prove that, under certain conditions, this prognostic covariate adjustment procedure attains the minimum variance possible among a large class of estimators. When those conditions are not met, prognostic covariate adjustment is still more efficient than raw covariate adjustment and the gain in efficiency is proportional to a measure of the predictive accuracy of the prognostic model. We demonstrate the approach using simulations and a reanalysis of an Alzheimer's Disease clinical trial and observe meaningful reductions in mean-squared error and the estimated variance. Lastly, we provide a simplified formula for asymptotic variance that enables power and sample size calculations that account for the gains from the prognostic model for clinical trial design.

Extreme precipitation events, such as violent rainfall and hail storms, routinely ravage economies and livelihoods around the developing world. Climate change further aggravates this issue. Data-driven deep learning approaches could widen the access to accurate multi-day forecasts, to mitigate against such events. However, there is currently no benchmark dataset dedicated to the study of global precipitation forecasts. In this paper, we introduce \textbf{RainBench}, a new multi-modal benchmark dataset for data-driven precipitation forecasting. It includes simulated satellite data, a selection of relevant meteorological data from the ERA5 reanalysis product, and IMERG precipitation data. We also release \textbf{PyRain}, a library to process large precipitation datasets efficiently. We present an extensive analysis of our novel dataset and establish baseline results for two benchmark medium-range precipitation forecasting tasks. Finally, we discuss existing data-driven weather forecasting methodologies and suggest future research avenues.

We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems. The setting we consider involves rank-one sensing matrices: In particular, given a set of rank-one projections of an approximately low-rank PSD matrix, we characterize the radius of the set of PSD matrices that satisfy the measurements. This result yields a sampling rate to guarantee singleton solution sets when the true matrix is exactly low-rank, such that the choice of the objective function or the algorithm to be used is inconsequential in its recovery. We discuss applications of this contribution and compare it to recent literature regarding implicit regularization for similar problems. We demonstrate practical implications of this result by applying conic projection methods for PSD matrix recovery without incorporating low-rank regularization.