Related papers: Consistent Estimation for Partition-wise Regressio…
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods.…
Methods for split conformal prediction leverage calibration samples to transform any prediction rule into a set-prediction rule that complies with a target coverage probability. Existing methods provide remarkably strong performance…
Deep learning models have shown promising results in a wide range of computer vision applications across various domains. The success of deep learning methods relies heavily on the availability of a large amount of data. Deep neural…
We study a non-parametric approach to multivariate density estimation. The estimators are piecewise constant density functions supported by binary partitions. The partition of the sample space is learned by maximizing the likelihood of the…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Conformal methods create prediction bands that control average coverage assuming solely i.i.d. data. Although the literature has mostly focused on prediction intervals, more general regions can often better represent uncertainty. For…
This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
Data splitting divides data into two parts. One part is reserved for model selection. In some applications, the second part is used for model validation but we use this part for estimating the parameters of the chosen model. We focus on the…
We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed…
We introduce a new methodology for analyzing serial data by quantile regression assuming that the underlying quantile function consists of constant segments. The procedure does not rely on any distributional assumption besides serial…
In this work we present full Bayesian inference for a new flexible nonseparable class of cross-covariance functions for multivariate spatial data. A Bayesian test is proposed for separability of covariance functions which is much more…
We provide a general mathematical framework for selective inference with supervised model selection procedures characterized by quadratic forms in the outcome variable. Forward stepwise with groups of variables is an important special case…
Variational inference (VI) has become the method of choice for fitting many modern probabilistic models. However, practitioners are faced with a fragmented literature that offers a bewildering array of algorithmic options. First, the…
In this paper, given a random uniform distribution of sensor nodes on a 2-D plane, a fast self-organized distributed algorithm is proposed to find the maximum number of partitions of the nodes such that each partition is connected and…
Robust validation of Machine Learning (ML) models is essential, but traditional data partitioning approaches often ignore the intrinsic quality of each instance. This study proposes the use of Item Response Theory (IRT) parameters to…
We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…
Vector autoregressive (VAR) models are popularly adopted for modelling high-dimensional time series, and their piecewise extensions allow for structural changes in the data. In VAR modelling, the number of parameters grow quadratically with…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…