相关论文: A Large Deviation Inequality for $\beta$-mixing Ti…

In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…

We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent…

Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…

Deep time-series forecasting can be formulated as a distribution balancing problem aimed at aligning the distribution of the forecasts and ground truths. According to Imbens' criterion, true distribution balance requires matching the first…

Let $(X_1,\ldots,X_n)$ be an i.i.d. sequence of random variables in $\mathbb{R}^d$, $d\geq 1$. We show that, for any function $\varphi :\mathbb{R}^d\rightarrow\mathbb{R}$, under regularity conditions, \[n^…

In this paper, we study various models for random combinatorial partitions using large deviation analysis for diverging scale of the reference process. Scaling limits of similar models have been studied recently \cite{FSa,FSb} going back to…

Multivariate conformal prediction requires nonconformity scores that compress residual vectors into scalars while preserving certain implicit geometric structure of the residual distribution. We introduce a Multivariate Kernel Score (MKS)…

Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional…

Consider $\beta > 1$ and $\lfloor \beta \rfloor$ its integer part. It is widely known that any real number $\alpha \in \Bigl[0, \frac{\lfloor \beta \rfloor}{\beta - 1}\Bigr]$ can be represented in base $\beta$ using a development in series…

We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…

Mixtures of linear mixed models are widely used for modelling longitudinal data for which observation times differ between subjects. In typical applications, temporal trends are described using a basis expansion, with basis coefficients…

In this paper we establish a large deviations type estimate for strongly mixing Markov chains with respect to the Lp norm. As applications we derive such estimates for the iterates of a locally constant random cocycle with mixed rank, as…

Smooth Estimation of probability density and distribution functions from its sample is an attractive and an important problem that has applications in several fields such as, business, medicine, and environment. This article introduces a…

In this paper, we are interested in nonparametric kernel estimation of a generalized regression function, including conditional cumulative distribution and conditional quantile functions, based on an incomplete sample $(X_t, Y_t,…

Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing…

In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…

Reliable prediction of protein variant effects is crucial for both protein optimization and for advancing biological understanding. For practical use in protein engineering, it is important that we can also provide reliable uncertainty…

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…

Various mixing conditions have been imposed on high dimensional time series, including the strong mixing ($\alpha$-mixing), maximal correlation coefficient ($\rho$-mixing), absolute regularity ($\beta$-mixing), and $\phi$-mixing.…