Related papers: Optimal rates for F-score binary classification
We characterize the minimax rate of estimating the second-order calibration error for binary classification, which quantifies whether a higher-order predictor's epistemic-uncertainty estimate matches the conditional variance of the label…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…
The F-measure is a widely used performance measure for multi-label classification, where multiple labels can be active in an instance simultaneously (e.g. in image tagging, multiple tags can be active in any image). In particular, the…
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…
Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet…
We consider the multivariate max-linear regression problem where the model parameters $\boldsymbol{\beta}_{1},\dotsc,\boldsymbol{\beta}_{k}\in\mathbb{R}^{p}$ need to be estimated from $n$ independent samples of the (noisy) observations $y =…
The data processing inequality is an information-theoretic principle stating that the information content of a signal cannot be increased by processing the observations. In particular, it suggests that there is no benefit in enhancing the…
We study the classical binary classification problem for hypothesis spaces of Deep Neural Networks (DNNs) under Tsybakov's low-noise condition with exponent $q>0$, as well as its limit case $q=\infty$, which we refer to as the \emph{hard…
A variety of different performance metrics are commonly used in the machine learning literature for the evaluation of classification systems. Some of the most common ones for measuring quality of hard decisions are standard and balanced…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
F-measures are popular performance metrics, particularly for tasks with imbalanced data sets. Algorithms for learning to maximize F-measures follow two approaches: the empirical utility maximization (EUM) approach learns a classifier having…
We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = X beta + z, then we suggest estimating the regression…
Feature selection aims to select the smallest subset of features for a specified level of performance. The optimal achievable classification performance on a feature subset is summarized by its Receiver Operating Curve (ROC). When infinite…
Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive…
Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…
Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLE) of regression parameters. For such data, a binary regression model incorporating misclassification probabilities is extensively…
We study sequential testing for a binary disease outcome when risk follows an unknown logistic model. At each round, the decision maker may either pay for a test revealing the true label or predict the outcome based on patient features and…
We discuss a method to improve the exact F-measure maximization algorithm called GFM, proposed in (Dembczynski et al. 2011) for multi-label classification, assuming the label set can be can partitioned into conditionally independent subsets…
Sparse additive models are families of $d$-variate functions that have the additive decomposition $f^* = \sum_{j \in S} f^*_j$, where $S$ is an unknown subset of cardinality $s \ll d$. In this paper, we consider the case where each…