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We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…
Accurate prediction of pedestrians' future motions is critical for intelligent driving systems. Developing models for this task requires rich datasets containing diverse sets of samples. However, the existing naturalistic trajectory…
Monitoring forecasting systems is critical for customer satisfaction, profitability, and operational efficiency in large-scale retail businesses. We propose The Forecast Critic, a system that leverages Large Language Models (LLMs) for…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
We investigate the financial market dynamics by introducing a heterogeneous agent-based opinion formation model. In this work, we organize the individuals in a financial market by their trading strategy, namely noise traders and…
We re-visit tail the index regressions framework. For linear specifications, we find that the usual full rank condition can fail because conditioning on extreme outcomes causes regressors to degenerate to constants. Taking this into…
The goal of developing a firmer theoretical understanding of inhomogenous temporal processes -- in particular, the waiting times in some collective dynamical system -- is attracting significant interest among physicists. Quantifying the…
Needless to say, linear dynamics are pervasive in economic time series, particularly autoregressive ones. While gradient boosting with trees excels at capturing nonlinearities, it is inefficient in small samples when much of the predictive…
Transformer-based architectures have achieved remarkable success in natural language processing and computer vision. However, their performance in multivariate long-term forecasting often falls short compared to simpler linear baselines.…
We consider the problem of constructing a regression model with a functional predictor and a functional response. We extend the functional linear model to the quadratic model, where the quadratic term also takes the interaction between the…
Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio…
Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…
This article develops flexible methodology to study the association between scalar outcomes and functional predictors observed over time, at many instances, in longitudinal studies. We propose a parsimonious modeling framework to study…
Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…
The leverage effect refers to the well-established relationship between returns and volatility. When returns fall, volatility increases. We examine the role of the leverage effect with regards to generating density forecasts of equity…
Pretraining data has a direct impact on the behaviors and quality of language models (LMs), but we only understand the most basic principles of this relationship. While most work focuses on pretraining data's effect on downstream task…
We revisit the Follow the Regularized Leader (FTRL) framework for Online Convex Optimization (OCO) over compact sets, focusing on achieving dynamic regret guarantees. Prior work has highlighted the framework's limitations in dynamic…
We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it…
Average forecast accuracy is not the same as forecast reliability. I treat forecast loss differentials relative to a benchmark as a return series. I then evaluate these returns using risk-adjusted performance measures from finance,…