arXiv research

A faster X-ray CT image reconstruction method using relaxed linearized algorithms.

New method improves neural network verification by considering multivariate input space of ReLU neurons.

Convex relaxations improve CNNs with fixed weights.

Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficul…

Differentiable relaxation for inferring partial orders from noisy linear data.

LP relaxations often provide tight solutions in structured prediction tasks.

Efficiently solves exploration-exploitation in LQR using Lagrangian relaxation.

Efficient online control algorithms for noisy systems with quadratic losses.

This work analyzes machine learning for Lagrangian Relaxation in MILP.

New method CROWN-IBP combines IBP and CROWN for efficient verifiable robust neural networks.

New conic relaxations improve sparse signal recovery with fewer observations.

Paper relaxes optimal transport using convex functions for data science.

New method controls linear systems with adversarial disturbances.

We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a…

Paper solves NP-hard sparse mixed linear regression problem with provable guarantees.

Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this paper, we study the statistical limits of convex relaxations. Particularly, we con…

Polynomial-time algorithm learns latent-state systems without spectral radius assumptions.

MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence…

Improved neural network robustness certification through tighter convex relaxations.

We optimize saddle-point problems for large-scale Markov decision processes.

Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.

The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a third observed multinomial distribution. We study the entire relaxation path for thi…

This work interprets SFA through variational inference, relaxing linearity constraints.

Renet improves Elastic Net by dynamically selecting between convex blending and refitting, enhancing prediction accuracy.

PEREGRiNN verifies safety of ReLU NNs by penalizing relaxation in a greedy manner.

A new method for efficient causal structure learning at scale.

New method closes certification gap for adversarially trained models.

Extends neural network verification to non-linear specifications.

We consider the problem of computing upper and lower bounds on the price of a European basket call option, given prices on other similar baskets. Although this problem is very hard to solve exactly in the general case, we show that in some instances the upper and lower bounds can be computed via simple closed-form expr…

Paper certifies k-means clustering optimality efficiently.

New conic quadratic formulations improve outlier detection in regression models.

We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.

Switching linear dynamics improves model-based reinforcement learning and system identification.

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach…

A nearly tight convex relaxation for sparse Naive Bayes features.

New method improves volatility forecasts by relaxing linear assumption in leverage effect.

New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.

We show that the spectral norm of a random $n_1\times n_2\times \cdots \times n_K$ tensor (or higher-order array) scales as $O\left(\sqrt{(\sum_{k=1}^{K}n_k)\log(K)}\right)$ under some sub-Gaussian assumption on the entries. The proof is based on a covering number argument. Since the spectral norm is dual to the tensor…

Paper uses ensemble learning for more accurate power flow modeling.

New method solves subspace optimization problems efficiently.

This work optimizes RL algorithms using entropy regularisation for continuous-time LQ problems.

Extracts transformations from images without supervision.

Improved clustering with outlier detection using cardinality constraints.

Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allo…

Improved Top-N recommendations with novel rank approximation.

The paper offers streamlined algorithms for fitting complex linear mixed models.

Study bounds financial path expectations using martingale distributions.

New methods optimize sums of bivariate functions on finite domains.