We formulate the sparse classification problem of n samples with p features as a binary convex optimization and propose outer-approximation algorithm to solve it exactly. For logistic regression SVM, our finds optimal solutions for in 10,000 s within minutes. On synthetic data achieves perfect support recovery large sample regime. Namely, there exists an $$n_0$$ such that takes long time find s...

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization (BO). Whilst the current methods provide desired approximations regression problems, it is observed that this particular form generates an overconfident GP, i.e., produces less epistemic uncertainty than original GP. Since balance between predictive mean and variance key determinant to s...

The CUR decomposition provides an approximation of a matrix X that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of X. In this regard, it appears to be similar to many sparse PCA methods. However, CUR takes a randomized algorithmic approach, whereas most sparse PCA methods are framed as convex optimization pr...

Many statistical machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. In this paper, we study this fundamental tradeoff through a SQRT-Lasso problem for sparse linear regression and sparse precision matrix estimation in high dimensions. We explain how novel optimization techniques help address these computational chall...

The state-of-the-art modern pose-graph optimization (PGO) systems are vertex based. In this context the number of variables might be high, albeit cycles in graph (loop closures) is relatively low. For sparse problems particularly, cycle space has a significantly smaller dimension than vertices. By exploiting observation, paper we propose an alternative solution to PGO, that directly exploits sp...