Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of future events as a means to improve decision making quality, and enhance social welfare. However, if maximizing welfare is the ultimate goal, prediction is only a small piece of the puzzle. There are various other policy levers a social planner might pursue in order to improve bottom-line outcomes, such as expanding access to available goods, or increasing the effect sizes of interventions. Given this broad range of design decisions, a basic question to ask is: What is the relative value of prediction in algorithmic decision making? How do the improvements in welfare arising from better predictions compare to those of other policy levers? The goal of our work is to initiate the formal study of these questions. Our main results are theoretical in nature. We identify simple, sharp conditions determining the relative value of prediction vis-\`a-vis expanding access, within several statistical models that are popular amongst quantitative social scientists. Furthermore, we illustrate how these theoretical insights may be used to guide the design of algorithmic decision making systems in practice.

Reinforcement learning (RL) theory has largely focused on proving minimax sample complexity bounds. These require strategic exploration algorithms that use relatively limited function classes for representing the policy or value function. Our goal is to explain why deep RL algorithms often perform well in practice, despite using random exploration and much more expressive function classes like neural networks. Our work arrives at an explanation by showing that many stochastic MDPs can be solved by performing only a few steps of value iteration on the random policy's Q function and then acting greedily. When this is true, we find that it is possible to separate the exploration and learning components of RL, making it much easier to analyze. We introduce a new RL algorithm, SQIRL, that iteratively learns a near-optimal policy by exploring randomly to collect rollouts and then performing a limited number of steps of fitted-Q iteration over those rollouts. Any regression algorithm that satisfies basic in-distribution generalization properties can be used in SQIRL to efficiently solve common MDPs. This can explain why deep RL works neural networks, since it is empirically established that neural networks generalize well in-distribution. Furthermore, SQIRL explains why random exploration works well in practice, since we show many environments can be solved by estimating the random policy's Q-function and then applying zero or a few steps of value iteration. We leverage SQIRL to derive instance-dependent sample complexity bounds for RL that are exponential only in an "effective horizon" of lookahead and on the complexity of the class used for function approximation. Empirically, we also find that SQIRL performance strongly correlates with PPO and DQN performance in a variety of stochastic environments, supporting that our theoretical analysis is predictive of practical performance.

In scenarios where obtaining real-time labels proves challenging, conventional approaches may result in sub-optimal performance. This paper presents an optimal strategy for streaming contexts with limited labeled data, introducing an adaptive technique for unsupervised regression. The proposed method leverages a sparse set of initial labels and introduces an innovative drift detection mechanism to enable dynamic model adaptations in response to evolving patterns in the data. To enhance adaptability, we integrate the ADWIN (ADaptive WINdowing) algorithm with error generalization based on Root Mean Square Error (RMSE). ADWIN facilitates real-time drift detection, while RMSE provides a robust measure of model prediction accuracy. This combination enables our multivariate method to effectively navigate the challenges of streaming data, continuously adapting to changing patterns while maintaining a high level of predictive precision. Finally, we evaluate the performance of our multivariate method across various public datasets, comparing it to non-adapting baselines. Through comprehensive assessments, we demonstrate the superior efficacy of our adaptive regression technique for tasks where obtaining labels in real-time is a significant challenge. The results underscore the method's capacity to outperform traditional approaches and highlight its potential in scenarios characterized by label scarcity and evolving data patterns.

The South Australia region of the Australian National Electricity Market (NEM) displays some of the highest levels of price volatility observed in modern electricity markets. This paper outlines an approach to probabilistic forecasting under these extreme conditions, including spike filtration and several post-processing steps. We propose using quantile regression as an ensemble tool for probabilistic forecasting, with our combined forecasts achieving superior results compared to all constituent models. Within our ensemble framework, we demonstrate that averaging models with varying training length periods leads to a more adaptive model and increased prediction accuracy. The applicability of the final model is evaluated by comparing our median forecasts with the point forecasts available from the Australian NEM operator, with our model outperforming these NEM forecasts by a significant margin.

Forecast combination involves using multiple forecasts to create a single, more accurate prediction. Recently, feature-based forecasting has been employed to either select the most appropriate forecasting models or to optimize the weights of their combination. In this paper, we present a multi-task optimization paradigm that focuses on solving both problems simultaneously and enriches current operational research approaches to forecasting. In essence, it incorporates an additional learning and optimization task into the standard feature-based forecasting approach, focusing on the identification of an optimal set of forecasting methods. During the training phase, an optimization model with linear constraints and quadratic objective function is employed to identify accurate and diverse methods for each time series. Moreover, within the training phase, a neural network is used to learn the behavior of that optimization model. Once training is completed the candidate set of methods is identified using the network. The proposed approach elicits the essential role of diversity in feature-based forecasting and highlights the interplay between model combination and model selection when optimizing forecasting ensembles. Experimental results on a large set of series from the M4 competition dataset show that our proposal enhances point forecast accuracy compared to state-of-the-art methods.

Partial Least-Squares (PLS) Regression is a widely used tool in chemometrics for performing multivariate regression. PLS is a bi-linear method that has a limited capacity of modelling non-linear relations between the predictor variables and the response. Kernel PLS (K-PLS) has been introduced for modelling non-linear predictor-response relations. In K-PLS, the input data is mapped via a kernel function to a Reproducing Kernel Hilbert space (RKH), where the dependencies between the response and the input matrix are assumed to be linear. K-PLS is performed in the RKH space between the kernel matrix and the dependent variable. Most available studies use fixed kernel parameters. Only a few studies have been conducted on optimizing the kernel parameters for K-PLS. In this article, we propose a methodology for the kernel function optimization based on Kernel Flows (KF), a technique developed for Gaussian process regression (GPR). The results are illustrated with four case studies. The case studies represent both numerical examples and real data used in classification and regression tasks. K-PLS optimized with KF, called KF-PLS in this study, is shown to yield good results in all illustrated scenarios. The paper presents cross-validation studies and hyperparameter analysis of the KF methodology when applied to K-PLS.

Monocular 3D human pose estimation (3D-HPE) is an inherently ambiguous task, as a 2D pose in an image might originate from different possible 3D poses. Yet, most 3D-HPE methods rely on regression models, which assume a one-to-one mapping between inputs and outputs. In this work, we provide theoretical and empirical evidence that, because of this ambiguity, common regression models are bound to predict topologically inconsistent poses, and that traditional evaluation metrics, such as the MPJPE, P-MPJPE and PCK, are insufficient to assess this aspect. As a solution, we propose ManiPose, a novel manifold-constrained multi-hypothesis model capable of proposing multiple candidate 3D poses for each 2D input, together with their corresponding plausibility. Unlike previous multi-hypothesis approaches, our solution is completely supervised and does not rely on complex generative models, thus greatly facilitating its training and usage. Furthermore, by constraining our model to lie within the human pose manifold, we can guarantee the consistency of all hypothetical poses predicted with our approach, which was not possible in previous works. We illustrate the usefulness of ManiPose in a synthetic 1D-to-2D lifting setting and demonstrate on real-world datasets that it outperforms state-of-the-art models in pose consistency by a large margin, while still reaching competitive MPJPE performance.

This paper studies robust nonparametric regression, in which an adversarial attacker can modify the values of up to $q$ samples from a training dataset of size $N$. Our initial solution is an M-estimator based on Huber loss minimization. Compared with simple kernel regression, i.e. the Nadaraya-Watson estimator, this method can significantly weaken the impact of malicious samples on the regression performance. We provide the convergence rate as well as the corresponding minimax lower bound. The result shows that, with proper bandwidth selection, $\ell_\infty$ error is minimax optimal. The $\ell_2$ error is optimal with relatively small $q$, but is suboptimal with larger $q$. The reason is that this estimator is vulnerable if there are many attacked samples concentrating in a small region. To address this issue, we propose a correction method by projecting the initial estimate to the space of Lipschitz functions. The final estimate is nearly minimax optimal for arbitrary $q$, up to a $\ln N$ factor.

Privacy of data has become increasingly important in large-scale machine learning applications, where data points correspond to individuals that seek privacy. Classifiers are often trained over data of individuals with sensitive attributes about individuals: income, education, marital status, and so on for instance. A wellaccepted way to incorporate privacy into machine learning is the framework of differential privacy [9, 7, 10]. The key idea is to add noise either to individual data items or to the output of the classifier so that the distribution of classifiers produced is mathematically close when an arbitrary individual is added or removed from the dataset. This provides a quantifiable way in which sensitive data about any individual is information theoretically secure during the classification process. All this comes at a cost: Adding noise leads to a loss in accuracy of the classifier, and as we elaborate below, a large body of work has studied the privacy-accuracy trade-off both theoretically and empirically.

In this paper, we consider a theoretical model for injecting data bias, namely, under-representation and label bias (Blum & Stangl, 2019). We empirically study the effect of varying data biases on the accuracy and fairness of fair classifiers. Through extensive experiments on both synthetic and real-world datasets (e.g., Adult, German Credit, Bank Marketing, COMPAS), we empirically audit pre-, in-, and post-processing fair classifiers from standard fairness toolkits for their fairness and accuracy by injecting varying amounts of under-representation and label bias in their training data (but not the test data). Our main observations are: 1. The fairness and accuracy of many standard fair classifiers degrade severely as the bias injected in their training data increases, 2. A simple logistic regression model trained on the right data can often outperform, in both accuracy and fairness, most fair classifiers trained on biased training data, and 3. A few, simple fairness techniques (e.g., reweighing, exponentiated gradients) seem to offer stable accuracy and fairness guarantees even when their training data is injected with under-representation and label bias. Our experiments also show how to integrate a measure of data bias risk in the existing fairness dashboards for real-world deployments.