We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer models with semi-random features, we prove with no unrealistic assumptions that the m…
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18 results for “semi-random”
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies heavily on the assumption that every entry is observed with exactly the same pro…
Paper tackles ranking items with a semi-random comparison graph and a monotone adversary.
problem Ranking items based on pairwise comparisons from a semi-random comparison graph with a monotone adversary.
method Developed a weighted maximum likelihood estimator (MLE) and an SDP-based approach to reweight the semi-random graph.
result Achieves near-optimal sample complexity, up to a log^2(n) factor, for identifying the top-K preferred items.
Spectral ranking methods are improved against semi-random graph sampling.
problem Improving spectral ranking methods in semi-random graph sampling.
method Investigating entry-wise error of spectral algorithms against a semi-random adversary.
result Asymptotic performance can be recovered by reweighting observed edges.
New method robust to semi-random sparse recovery, nearly-linear time.
problem Brittleness of fast sparse recovery algorithms under generative model changes.
method Designing a new iterative method robust to semi-random model.
result Proves robustness of new method to semi-random generative models.
KSS method converges and recovers correct clustering under certain conditions.
problem Subspace clustering for semi-randomly sampled data.
method Local convergence analysis and recovery guarantee for KSS method.
result KSS method converges superlinearly and finds correct clustering within loglog N iterations.
Hidden Integrality and Semi-random Robustness of SDP Relaxation for Sub-Gaussian Mixture Modelstat.ML
We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while the optimal solution to the SDP is not integer-valued in general, its estimation …
Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are relatively robust to random noise. In this paper, we propose to study a \textit{semi-ran…
This work proposes a non-iterative strategy for missing value imputations which is guided by similarity between observations, but instead of explicitly determining distances or nearest neighbors, it assigns observations to overlapping buckets through recursive semi-random hyperplane cuts, in which weighted averages are…
Efficient exploration is an unsolved problem in Reinforcement Learning which is usually addressed by reactively rewarding the agent for fortuitously encountering novel situations. This paper introduces an efficient active exploration algorithm, Model-Based Active eXploration (MAX), which uses an ensemble of forward mod…
Improved SGD for robust linear and ReLU regression with adversarial corruptions.
problem Robust regression with adversarial corruptions in streaming data.
method Stochastic gradient descent (SGD-exp) with exponentially decaying step size.
result Nearly linear convergence to true parameter with up to 50% Massart corruption rate.
Efficient algorithm detects communities in noisy graphs with robustness.
problem Community detection in stochastic block models with adversarial corruptions.
method Efficient algorithm using semidefinite programming for robust clustering.
result Achieves error for -fraction of corruptions.
Study on ReLU regression with Massart noise, achieving exact parameter recovery.
problem Efficiently fitting ReLUs to data in the presence of Massart noise.
method Developed an efficient algorithm for exact parameter recovery under mild assumptions.
result Achieved exact parameter recovery in ReLU regression with Massart noise.
Improved Graph Clusteringstat.ML
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this problem is the stochastic block model, also referred to as the planted partition model…
Semi-Supervised Nonlinear Distance Metric Learning via Forests of Max-Margin Cluster Hierarchiesstat.ML
Metric learning is a key problem for many data mining and machine learning applications, and has long been dominated by Mahalanobis methods. Recent advances in nonlinear metric learning have demonstrated the potential power of non-Mahalanobis distance functions, particularly tree-based functions. We propose a novel non…
Paper improves -SSC for noisy data by proving SDP and proposing Noisy-DR--SSC.
problem Noisy data and less restrictive subspace affinity in sparse subspace clustering.
method Proposes Noisy-DR--SSC, which projects data onto a lower dimensional space and then applies noisy -SSC.
result Theoretical guarantee on the correctness of noisy -SSC in terms of SDP on noisy data.
This paper improves linear system solving by optimizing matrix diagonal scaling.
problem Improving the condition number of a matrix for faster iterative methods.
method Left or right diagonal rescaling of the matrix A, with new bounds and algorithms.
result Jacobi preconditioning reduces A's condition number to within a quadratic factor of the best possible scaling.
New formula refutes random CSPs with fewer constraints.
problem Refuting random constraint satisfaction problems efficiently.
method Introduced a non-backtracking matrix and proved an Ihara-Bass formula.
result Efficiently refutes random CSPs with fewer constraints.