相关论文: Oracle inequalities for sign constrained generaliz…
Learning of matrix-valued data has recently surged in a range of scientific and business applications. Trace regression is a widely used method to model effects of matrix predictors and has shown great success in matrix learning. However,…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
In this paper, we study the issue of estimating a structured signal $x_0 \in \mathbb{R}^n$ from non-linear and noisy Gaussian observations. Supposing that $x_0$ is contained in a certain convex subset $K \subset \mathbb{R}^n$, we prove that…
We study various constraints and conditions on the true coefficient vector and on the design matrix to establish non-asymptotic oracle inequalities for the prediction error, estimation accuracy and variable selection for the Lasso estimator…
Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different conditions and concepts relate…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
We propose in this paper a general framework for deriving loss functions for structured prediction. In our framework, the user chooses a convex set including the output space and provides an oracle for projecting onto that set. Given that…
Structured sparsity is an important part of the modern statistical toolkit. We say a set of model parameters has block diagonal sparsity up to permutations if its elements can be viewed as the edges of a graph that has multiple connected…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
We propose a general method called truncated gradient to induce sparsity in the weights of online learning algorithms with convex loss functions. This method has several essential properties: The degree of sparsity is continuous -- a…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…
Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…
Efficient online learning with pairwise loss functions is a crucial component in building large-scale learning system that maximizes the area under the Receiver Operator Characteristic (ROC) curve. In this paper we investigate the…
The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research. Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we…
We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…