Related papers: Local shrinkage rules, Levy processes, and regular…
When faced with a supervised learning problem, we hope to have rich enough data to build a model that predicts future instances well. However, in practice, problems can exhibit predictive heterogeneity: most instances might be relatively…
During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derviative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood…
Use of continuous shrinkage priors -- with a "spike" near zero and heavy-tails towards infinity -- is an increasingly popular approach to induce sparsity in parameter estimates. When the parameters are only weakly identified by the…
If a document is about travel, we may expect that short snippets of the document should also be about travel. We introduce a general framework for incorporating these types of invariances into a discriminative classifier. The framework…
The method of Bayesian variable selection via penalized credible regions separates model fitting and variable selection. The idea is to search for the sparsest solution within the joint posterior credible regions. Although the approach was…
In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…
Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…
Global-local shrinkage hierarchies are an important innovation in Bayesian estimation. We propose the use of log-scale distributions as a novel basis for generating familes of prior distributions for local shrinkage hyperparameters. By…
We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding…
The generalized Langevin equation is used as a model for various coarse-grained physical processes, e.g., the time evolution of the velocity of a given larger particle in an implicitly represented solvent, when the relevant time scales of…
Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these…
Forecasting groups of time series is of increasing practical importance, e.g. forecasting the demand for multiple products offered by a retailer or server loads within a data center. The local approach to this problem considers each time…
We study the penalization problem with various clocks where the weight is given as the exponential functional of multi-point local times for one-dimensional L\'{e}vy processes. The limit processes may vary according to the choice of random…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…