Fish get bigger as they get older. How predictive is fish length (cm) with age (yr) as the explanatory variable? Is the relationship best fit with a linear regression? First, let's bring in the data and a few important modules for the analysis: There are 77 instances in the data set. Now let's visualize the scatter-plot.

Any solution to the "policy learning" problem needs to deal with numerous difficulties, including how to incorporate robustness to potential selection bias as well as fairness constraints articulated by stakeholders, and there have been several notable advances that address these difficulties over the past few years. One limitation of this line of work, however, is that the results cited above all focus on a static setting where a decision-maker only sees each subject once and immediately decides how to treat the subject. In contrast, many problems of applied interest involve a dynamic component whereby the decision-maker makes a series of decisions based on time-varying covariates. In medicine, if a patient has a disease for which all known cures are invasive and have serious side effects, their doctor may choose to monitor disease progression for some time before prescribing one of these invasive treatments. Meanwhile, a health inspector needs to not only choose which restaurants to inspect, but also when to carry out these inspections.

In developing countries like India agriculture plays an extremely important role in the lives of the population. In India, around 80\% of the population depend on agriculture or its by-products as the primary means for employment. Given large population dependency on agriculture, it becomes extremely important for the government to estimate market factors in advance and prepare for any deviation from those estimates. Commodity arrivals to market is an extremely important factor which is captured at district level throughout the country. Historical data and short-term prediction of important variables such as arrivals, prices, crop quality etc. for commodities are used by the government to take proactive steps and decide various policy measures. In this paper, we present a framework to work with short timeseries in conjunction with remote sensing data to predict future commodity arrivals. We deal with extremely high dimensional data which exceed the observation sizes by multiple orders of magnitude. We use cascaded layers of dimensionality reduction techniques combined with regularized regression models for prediction. We present results to predict arrivals to major markets and state wide prices for `Tur' (red gram) crop in Karnataka, India. Our model consistently beats popular ML techniques on many instances. Our model is scalable, time efficient and can be generalized to many other crops and regions. We draw multiple insights from the regression parameters, some of which are important aspects to consider when predicting more complex quantities such as prices in the future. We also combine the insights to generate important recommendations for different government organizations.

This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile loss poses new challenges to high-dimensional distributed estimation in both computation and theoretical development. To address the challenge, we transform the response variable and establish a new connection between quantile regression and ordinary linear regression. Then, we provide a distributed estimator that is both computationally and communicationally efficient, where only the gradient information is communicated at each iteration. Theoretically, we show that, after a constant number of iterations, the proposed estimator achieves a near-oracle convergence rate without any restriction on the number of machines. Moreover, we establish the theoretical guarantee for the support recovery. The simulation analysis is provided to demonstrate the effectiveness of our method.

We study the problem of safe learning and exploration in sequential control problems. The goal is to safely collect data samples from an operating environment to learn an optimal controller. A central challenge in this setting is how to quantify uncertainty in order to choose provably-safe actions that allow us to collect useful data and reduce uncertainty, thereby achieving both improved safety and optimality. To address this challenge, we present a deep robust regression model that is trained to directly predict the uncertainty bounds for safe exploration. We then show how to integrate our robust regression approach with model-based control methods by learning a dynamic model with robustness bounds. We derive generalization bounds under domain shifts for learning and connect them with safety and stability bounds in control. We demonstrate empirically that our robust regression approach can outperform conventional Gaussian process (GP) based safe exploration in settings where it is difficult to specify a good GP prior.

In many practical applications of contextual bandits, online learning is infeasible and practitioners must rely on off-policy evaluation (OPE) of logged data collected from prior policies. OPE generally consists of a combination of two components: (i) directly estimating a model of the reward given state and action and (ii) importance sampling. While recent work has made significant advances adaptively combining these two components, less attention has been paid to improving the quality of the importance weights themselves. In this work we present balancing off-policy evaluation (BOP-e), an importance sampling procedure that directly optimizes for balance and can be plugged into any OPE estimator that uses importance sampling. BOP-e directly estimates the importance sampling ratio via a classifier which attempts to distinguish state-action pairs from an observed versus a proposed policy. BOP-e can be applied to continuous, mixed, and multi-valued action spaces without modification and is easily scalable to many observations. Further, we show that minimization of regret in the constructed binary classification problem translates directly into minimizing regret in the off-policy evaluation task. Finally, we provide experimental evidence that BOP-e outperforms inverse propensity weighting-based approaches for offline evaluation of policies in the contextual bandit setting under both discrete and continuous action spaces.

We present pairwise metrics of fairness for ranking and regression models that form analogues of statistical fairness notions such as equal opportunity or equal accuracy, as well as statistical parity. Our pairwise formulation supports both discrete protected groups, and continuous protected attributes. We show that the resulting training problems can be efficiently and effectively solved using constrained optimization and robust optimization techniques based on two player game algorithms developed for fair classification. Experiments illustrate the broad applicability and trade-offs of these methods.

Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic regression are well understood. Recently, Sur and Candes have studied logistic regression in the high-dimensional regime, where the number of observations and parameters are comparable, and show, among other things, that the maximum likelihood estimator is biased. In the high-dimensional regime the underlying parameter vector is often structured (sparse, block-sparse, finite-alphabet, etc.) and so in this paper we study regularized logistic regression (RLR), where a convex regularizer that encourages the desired structure is added to the negative of the log-likelihood function. An advantage of RLR is that it allows parameter recovery even for instances where the (unconstrained) maximum likelihood estimate does not exist. We provide a precise analysis of the performance of RLR via the solution of a system of six nonlinear equations, through which any performance metric of interest (mean, mean-squared error, probability of support recovery, etc.) can be explicitly computed. Our results generalize those of Sur and Candes and we provide a detailed study for the cases of $\ell_2^2$-RLR and sparse ($\ell_1$-regularized) logistic regression. In both cases, we obtain explicit expressions for various performance metrics and can find the values of the regularizer parameter that optimizes the desired performance. The theory is validated by extensive numerical simulations across a range of parameter values and problem instances.

We study how language on social media is linked to diseases such as atherosclerotic heart disease (AHD), diabetes and various types of cancer. Our proposed model leverages state-of-the-art sentence embeddings, followed by a regression model and clustering, without the need of additional labelled data. It allows to predict community-level medical outcomes from language, and thereby potentially translate these to the individual level. The method is applicable to a wide range of target variables and allows us to discover known and potentially novel correlations of medical outcomes with life-style aspects and other socioeconomic risk factors.

In-game win probability is a statistical metric that provides a sports team's likelihood of winning at any given point in a game, based on the performance of historical teams in the same situation. In-game win-probability models have been extensively studied in baseball, basketball and American football. These models serve as a tool to enhance the fan experience, evaluate in game-decision making and measure the risk-reward balance for coaching decisions. In contrast, they have received less attention in association football, because its low-scoring nature makes it far more challenging to analyze. In this paper, we build an in-game win probability model for football. Specifically, we first show that porting existing approaches, both in terms of the predictive models employed and the features considered, does not yield good in-game win-probability estimates for football. Second, we introduce our own Bayesian statistical model that utilizes a set of eight variables to predict the running win, tie and loss probabilities for the home team. We train our model using event data from the last four seasons of the major European football competitions. Our results indicate that our model provides well-calibrated probabilities. Finally, we elaborate on two use cases for our win probability metric: enhancing the fan experience and evaluating performance in crucial situations.