Related papers: Optimal Ridge Detection using Coverage Risk
Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient…
We propose a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis and model based clustering. A ridge penalty and a ridge fusion penalty are used to introduce shrinkage and…
We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The…
A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
In many areas, practitioners need to analyze large datasets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental…
The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation…
In this paper, a new concept, radial coverage strength, is first proposed to characterize the visual sensing performance when the orientation of the target pose is considered. In particular, the elevation angle of the optical pose of the…
We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…
This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and sub-additive risk measures. We employ Mirror Descent algorithms to determine the optimal risk…
We study the risk (i.e. generalization error) of Kernel Ridge Regression (KRR) for a kernel $K$ with ridge $\lambda>0$ and i.i.d. observations. For this, we introduce two objects: the Signal Capture Threshold (SCT) and the Kernel Alignment…
We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size,…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying…
Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…
Ridge estimators regularize the squared Euclidean lengths of parameters. Such estimators are mathematically and computationally attractive but involve tuning parameters that can be difficult to calibrate. In this paper, we show that ridge…
Dynamic density estimation is ubiquitous in many applications, including computer vision and signal processing. One popular method to tackle this problem is the "sliding window" kernel density estimator. There exist various implementations…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
We provide a deterministic space-efficient algorithm for estimating ridge regression. For $n$ data points with $d$ features and a large enough regularization parameter, we provide a solution within $\varepsilon$ L$_2$ error using only…