Related papers: Convergence Rates for Empirical Estimation of Bina…
In the context of binary classification of trajectories generated by time-homogeneous stochastic differential equations, we consider a mixture of two diffusion processes characterized by a stochastic differential equation (SDE) whose drift…
Real networks often have severe degree heterogeneity, with the maximum, average, and minimum node degrees differing significantly. This paper examines the impact of degree heterogeneity on statistical limits of network data analysis.…
In this paper, an online learning algorithm is proposed as sequential stochastic approximation of a regularization path converging to the regression function in reproducing kernel Hilbert spaces (RKHSs). We show that it is possible to…
Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…
We consider the problem of estimating a $d$-dimensional discrete distribution from its samples observed under a $b$-bit communication constraint. In contrast to most previous results that largely focus on the global minimax error, we study…
We prove a rate of convergence for the $N$-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common…
In this paper, two new classes of lower bounds on the probability of error for $m$-ary hypothesis testing are proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP)…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework,…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with…
Reliable inference from complex survey samples can be derailed by outliers and high-leverage observations induced by unequal inclusion probabilities and calibration. We develop a minimum Hellinger distance estimator (MHDE) for parametric…
The hybrid censoring is a mixture of Type I and Type II censoring schemes. This paper presents the statistical inferences of the Inverse Weibull distribution when the data are Type-I hybrid censored. First we consider the maximum likelihood…
Bayesian classification labels observations based on given prior information, namely class-a priori and class-conditional probabilities. Bayes' risk is the minimum expected classification cost that is achieved by the Bayes' test, the…
We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…
We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…
Recently, learning with soft labels has been shown to achieve better performance than learning with hard labels in terms of model generalization, calibration, and robustness. However, collecting pointwise labeling confidence for all…
In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for…
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…
We study the problem of estimating the score function of an unknown probability distribution $\rho^*$ from $n$ independent and identically distributed observations in $d$ dimensions. Assuming that $\rho^*$ is subgaussian and has a…