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The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…
In this paper, we propose a cost function that corresponds to the mean square errors between estimated values and true values of conditional probability in a discrete distribution. We then obtain the values that minimize the cost function.…
A successful deep learning network is highly dependent not only on the training dataset, but the training algorithm used to condition the network for a given task. The loss function, dataset, and tuning of hyperparameters all play an…
The forecasting of the credit default risk has been an important research field for several decades. Traditionally, logistic regression has been widely recognized as a solution due to its accuracy and interpretability. As a recent trend,…
Traditional machine learning methods usually minimize a simple loss function to learn a predictive model, and then use a complex performance measure to measure the prediction performance. However, minimizing a simple loss function cannot…
The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…
We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and…
This paper introduces a framework for estimating fair optimal predictions using machine learning where the notion of fairness can be quantified using path-specific causal effects. We use a recently developed approach based on Lagrange…
Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively…
The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine…
The beneficial effects of treatments vary across individuals in most studies. Treatment heterogeneity motivates practitioners to search for the optimal policy based on personal characteristics. A long-standing common practice in policy…
Modern statistical analysis often encounters high-dimensional problems but with a limited sample size. It poses great challenges to traditional statistical estimation methods. In this work, we adopt auxiliary learning to solve the…
Significant advances have been made recently on training neural networks, where the main challenge is in solving an optimization problem with abundant critical points. However, existing approaches to address this issue crucially rely on a…
Deep learning has achieved impressive performance on many tasks in recent years. However, it has been found that it is still not enough for deep neural networks to provide only point estimates. For high-risk tasks, we need to assess the…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on…
While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in…
Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…