Improved Compressed Sensing by optimizing sparse solutions with mixed integer programming.
problem Finding sparse solutions to linear measurements with numerical tolerance.
method Introducing an ℓ2 regularized formulation, reformulating as a mixed integer second order cone program, deriving a second order cone relaxation, and developing a custom branch-and-bound algorithm. result Our approach produces solutions that are on average 6.22% more sparse compared to state-of-the-art methods.
Study optimal consumption with relaxed benchmarks and drawdown constraints.
problem Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint.
method Transformed stochastic control problem into regular control problem with state-control constraints, then solved using dual transform and optimal consumption behavior.
result Closed-form solution for optimal investment and consumption in feedback form.
New algorithms achieve better regret bounds for online classification with relaxed benchmarks.
problem Competing with worst-case optimal binary loss in online classification.
method Comparing against predictors robust to small input perturbations, performing well under Gaussian smoothing, or maintaining a prescribed output margin.
result Regret guarantees depend only on VC dimension and instance space complexity, with an O(log(1/γ)) dependence on the generalized margin. The paper solves a control problem using reflections to track a benchmark process.
problem Optimal consumption with a benchmark process that grows over time.
method Introduced two auxiliary state processes with reflections to transform the problem into a more tractable form.
result Established the existence of a unique classical solution to the dual PDE.
Bayesian learning is often hampered by large computational expense. As a powerful generalization of popular belief propagation, expectation propagation (EP) efficiently approximates the exact Bayesian computation. Nevertheless, EP can be sensitive to outliers and suffer from divergence for difficult cases. To address t…
RLSbench benchmarks domain adaptation under label proportion shifts, revealing widespread failures and proposing a two-step meta-algorithm.
problem Domain adaptation under label proportion shifts is poorly understood and inconsistent across methods.
method RLSbench introduces a large-scale benchmark with 500 distribution shift pairs. It proposes a two-step meta-algorithm to improve domain adaptation methods under label proportion shifts.
result The two-step meta-algorithm improves domain adaptation methods by 2-10% accuracy points under large label proportion shifts.
New method for sparse kernel selection improves prediction accuracy.
problem Sparse Multiple Kernel Learning for binary classification.
method Alternating best response algorithm with semidefinite relaxations.
result Method outperforms state-of-the-art MKL approaches in prediction accuracy.
New dataset abla2DFT for drug-like molecules benchmarks neural network potentials.
problem Lack of large, diverse datasets for training neural network potentials in quantum chemistry.
method Developed a new dataset abla2DFT containing energies, forces, and molecular properties for drug-like molecules. result First dataset with relaxation trajectories for drug-like molecules.
Verification of neural networks enables us to gauge their robustness against adversarial attacks. Verification algorithms fall into two categories: exact verifiers that run in exponential time and relaxed verifiers that are efficient but incomplete. In this paper, we unify all existing LP-relaxed verifiers, to the best…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational dif…
Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work (Jang et al. 2016, Maddison et al. 2016) has taken a different approach, introducing a continuou…
Improves scalability of Bayesian optimization for combinatorial spaces.
problem Optimizing expensive functions over large combinatorial spaces.
method Parametrized Submodular Relaxation (PSR) to solve AFO problems for BOCS.
result Significant improvements in scalability and accuracy for BOCS model.
Renet improves Elastic Net by dynamically selecting between convex blending and refitting, enhancing prediction accuracy.
problem Elastic Net's shrinkage bias limits its prediction accuracy in high-dimensional settings.
method Adaptive relaxation procedure that dynamically dispatches between convex blending and efficient sub-path refitting.
result Renet consistently outperforms standard Elastic Net and Adaptive Elastic Net in high-dimensional, low signal-to-noise ratio, and high-multicollinearity scenarios.
Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of real-world applications, which is known to be NP-hard for general graphs. In this paper, we propose a novel semidefinite relaxation formulation (referred to as SDR) to estimate the MAP assignment. A…
We generalize stochastic smoothing for gradient estimation of non-differentiable functions.
problem Gradient estimation for non-differentiable functions.
method Developed a general framework for relaxation and gradient estimation of non-differentiable black-box functions using stochastic smoothing with reduced assumptions.
result Empirically validated the effectiveness of variance reduction strategies for various non-differentiable tasks.
Bayesian framework for SSP problem learns optimal strategy through interactions.
problem Sequential decision-making in stochastic shortest path problems.
method Develops a Bayesian framework to learn optimal action-value function Q∗ through interactions, avoiding unrealistic assumptions. result Demonstrates data efficiency and uncertainty quantification compared to other methods.
Introduces optimization geometrodynamics for dynamic geometric optimization.
problem Gradient-based optimization methods struggle with changing geometric constraints.
method Optimization geometrodynamics separates invariant and improvable geometric mismatches.
result Dynamic geometric complexity measures the minimum geometric cost to reduce optimization difficulty.
We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled…
Study bounds financial path expectations using martingale distributions.
problem Bounding path-dependent financial expectations over martingale distributions.
method Relaxed martingale optimal transport problem, approximated via linear programming.
result Empirical relaxation can be approximated within O(n^(-1/2)) error.
We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this paper, we pose it as a combinatorial optimization problem, which is then relaxed to a…
Paper relaxes factor analysis for noisy data, improving robustness.
problem Challenges in finding robust low dimensional approximations for data with heteroskedastic noise.
method Introduces a relaxed version of Minimum Trace Factor Analysis (MTFA) as a convex optimization method.
result Effective at not overfitting to heteroskedastic perturbations and addressing common issues in factor analysis.
We propose a family of relaxations of the optimal transport problem which regularize the problem by introducing an additional minimization step over a small region around one of the underlying transporting measures. The type of regularization that we obtain is related to smoothing techniques studied in the optimization…
DOFEN improves DNN performance on tabular data benchmarks.
problem DOFEN tackles the performance gap between DNNs and tree-based models on tabular data.
method DOFEN uses a two-level rODT forest ensembling process inspired by oblivious decision trees.
result DOFEN achieves state-of-the-art results on the Tabular Benchmark.
The paper extends Merton's problem by adding benchmark tracking, finding optimal strategies.
problem Maximizing consumption utility with a trade-off against benchmark performance.
method Developed a convex duality theorem and derived optimal strategies for specific cases.
result Found optimal portfolio and consumption strategies for CRRA utility and geometric Brownian motion benchmarks.
Efficiently solves MRF inference problems with semidefinite programming.
problem Computing partition function or MAP estimate in binary and multi-class MRFs.
method Coordinate-descent-based fast semidefinite solver for SDPs.
result Substantially outperforms existing state-of-the-art methods in approximate inference.
New algorithms improve neural architecture search with faster convergence.
problem Improving efficiency and accuracy of neural architecture search.
method Geometry-aware gradient algorithms to optimize continuous relaxation of discrete search spaces.
result Exceeds state-of-the-art results on CIFAR and ImageNet benchmarks.
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a graph matching problem where one seeks a mapping between vertices of two graphs whic…
DisARM improves gradient estimation for binary latent variables.
problem Challenges in training models with discrete latent variables.
method Uses antithetic sampling over continuous augmentation.
result DisARM consistently outperforms ARM and baseline methods in log-likelihood and variance.
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an ℓ0 constraint restricting the support of the estimators is a challenging (\NP-hard) non-convex optimization problem. In this paper…
We study online prediction where regret of the algorithm is measured against a benchmark defined via evolving constraints. This framework captures online prediction on graphs, as well as other prediction problems with combinatorial structure. A key aspect here is that finding the optimal benchmark predictor (even in hi…
New method compares classifiers using GSD-front, addressing statistical uncertainty and robustness.
problem Comparing classifiers with multiple quality metrics and statistical uncertainty.
method Proposes GSD-front and statistical tests for robust comparisons.
result Reliable method for comparing classifiers with statistical uncertainty and robustness.
New MIP approach for efficient change-point detection.
problem Offline multiple change-point detection in data streams.
method Mixed-integer programming (MIP) for globally optimal PWL fitting.
result Provable tighter relaxations for segment assignment variables.
New gauge fields modify Fokker-Planck dynamics without changing the stationary state.
problem Understanding and modifying nonreversible dynamics in Fokker-Planck models.
method Formulate nonreversible perturbations as gauge fields, mapping to supersymmetric Hamiltonians, and learning finite forces.
result Learned finite forces can recover the optimal Lyapunov-equation solution in nonconvex landscapes.
Generalizes neural network verification by adding arbitrary cutting planes.
problem Handling general cutting plane constraints in neural network verification.
method Generalized bound propagation method (GCP-CROWN) that allows arbitrary cutting plane constraints.
result GCP-CROWN significantly improves neural network verification performance.
PAIR optimizes machine learning models to generalize better to out-of-distribution data.
problem Optimization of machine learning models for out-of-distribution (OOD) generalization often leads to compromises that weaken robustness.
method Introduces a multi-objective optimization (MOO) perspective and a new optimization scheme called PAreto Invariant Risk Minimization (PAIR).
result PAIR improves robustness of OOD objectives by cooperatively optimizing with other objectives, yielding top OOD performances.
Unified framework for fair regression in aware and unaware settings.
problem Lack of principled methods for fair regression in unawareness settings.
method Formulated as an optimal transport problem, unifying aware and unaware settings.
result Characterizes optimal prediction functions via optimal transport maps under different penalties.
New method improves neural network verification by considering multivariate input space of ReLU neurons.
problem Improving the effectiveness of neural network verification algorithms.
method A new tightened convex relaxation for ReLU neurons considering multivariate input space.
result Our convex relaxation is significantly stronger than the commonly used univariate-input relaxation.
Improved neural network robustness certification through tighter convex relaxations.
problem Certifying neural network robustness to perturbed and adversarial inputs.
method Exploiting ReLU network structure, novel partition-based certification procedure.
result Tightens existing linear programming relaxations to achieve zero relaxation error asymptotically.
In this note we compare two recently proposed semidefinite relaxations for the sparse linear regression problem by Pilanci, Wainwright and El Ghaoui (Sparse learning via boolean relaxations, 2015) and Dong, Chen and Linderoth (Relaxation vs. Regularization A conic optimization perspective of statistical variable select…
Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race between defenders who attempt to train robust networks and attackers who try to constr…
We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the glob…
A new method for hierarchical clustering using continuous embeddings and optimization.
problem Hierarchical clustering with provable quality guarantees.
method Continuous relaxation of discrete optimization problem using hyperbolic embeddings and decoding.
result Continuous relaxation yields a discrete tree with (1 + epsilon)-factor approximation for optimal tree.
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…
ShotgunCSP predicts crystal structures using machine learning, achieving high accuracy with minimal computation.
problem Predicting stable or metastable crystal structures of large systems.
method Noniterative screening using transfer learning and generative models.
result ShotgunCSP achieves 93.3% accuracy in benchmark tests with 90 different crystal structures.
RARTS improves neural architecture search efficiency and accuracy.
problem Efficiency and accuracy issues in first-order DARTS.
method Formulates a relaxed architecture search (RARTS) method that uses whole dataset splitting.
result RARTS outperforms DARTS and its variants in accuracy and efficiency.
Paper relaxes set-valued prediction in hierarchical classification by considering representation complexity.
problem Uncertainty in class labels in hierarchical multi-class classification problems.
method Introduces representation complexity for predicted sets, proposes three methods for inference.
result Recursive tree search method is computationally more efficient.
New control methods for systems with adversarial perturbations.
problem Control systems with adversarial noise.
method Online convex optimization and convex relaxations.
result Low regret policies against adversarial perturbations.
Multilabel classification is an important problem in a wide range of domains such as text categorization and music annotation. In this paper, we present a probabilistic model, Multilabel Logistic Regression with Hidden variables (MLRH), which extends the standard logistic regression by introducing hidden variables. Hid…