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Found 28 papers, 2 papers with code
Training Subset Selection for Weak Supervision
Subset selection applies to any label model and classifier and is very simple to plug in to existing weak supervision pipelines, requiring just a few lines of code.
Towards Learning Sparsely Used Dictionaries with Arbitrary Supports
To address this question while circumventing the issue of non-identifiability, we study a natural semirandom model for dictionary learning where there are a large number of samples $y=Ax$ with arbitrary k-sparse supports for x, along with a few samples where the sparse supports are chosen uniformly at random.
Optimality of Approximate Inference Algorithms on Stable Instances
Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances.
Clustering Stable Instances of Euclidean k-means
We design efficient algorithms that provably recover the optimal clustering for instances that are additive perturbation stable.
Clustering Semi-Random Mixtures of Gaussians
Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis.
On Learning Mixtures of Well-Separated Gaussians
In the most basic form of this problem, we are given samples from a uniform mixture of $k$ standard spherical Gaussians, and the goal is to estimate the means up to accuracy $\delta$ using $poly(k, d, 1/\delta)$ samples.
Learning Communities in the Presence of Errors
Many algorithms exist for learning communities in the Stochastic Block Model, but they do not work well in the presence of errors.
Correlation Clustering with Noisy Partial Information
In this paper, we propose and study a semi-random model for the Correlation Clustering problem on arbitrary graphs G. We give two approximation algorithms for Correlation Clustering instances from this model.
Learning Mixtures of Ranking Models
We present the first polynomial time algorithm which provably learns the parameters of a mixture of two Mallows models.
Constant Factor Approximation for Balanced Cut in the PIE model
Let $G$ be an arbitrary graph on $V$ with no edges between $L$ and $R$.
Smoothed Analysis of Tensor Decompositions
We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension).
Uniqueness of Tensor Decompositions with Applications to Polynomial Identifiability
We give a robust version of the celebrated result of Kruskal on the uniqueness of tensor decompositions: we prove that given a tensor whose decomposition satisfies a robust form of Kruskal's rank condition, it is possible to approximately recover the decomposition if the tensor is known up to a sufficiently small (inverse polynomial) error.
Block Stability for MAP Inference
The simplest stability condition assumes that the MAP solution does not change at all when some of the pairwise potentials are (adversarially) perturbed.
Smoothed Analysis in Unsupervised Learning via Decoupling
Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis.
Clustering Stable Instances of Euclidean k-means.
To address this disconnect, we study the following question: what properties of real-world instances will enable us to design efficient algorithms and prove guarantees for finding the optimal clustering?
On Robustness to Adversarial Examples and Polynomial Optimization
In particular, we leverage this connection to (a) design computationally efficient robust algorithms with provable guarantees for a large class of hypothesis, namely linear classifiers and degree-2 polynomial threshold functions (PTFs), (b) give a precise characterization of the price of achieving robustness in a computationally efficient manner for these classes, (c) design efficient algorithms to certify robustness and generate adversarial attacks in a principled manner for 2-layer neural networks.
Adversarially Robust Low Dimensional Representations
In particular, our adversarially robust PCA primitive leads to computationally efficient and robust algorithms for both unsupervised and supervised learning problems such as clustering and learning adversarially robust classifiers.
Estimating Principal Components under Adversarial Perturbations
We design a computationally efficient algorithm that given corrupted data, recovers an estimate of the top-$r$ principal subspace with error that depends on a robustness parameter $\kappa$ that we identify.
Adversarial robustness via robust low rank representations
Adversarial robustness measures the susceptibility of a classifier to imperceptible perturbations made to the inputs at test time.
Efficient Tensor Decomposition
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors.
Graph cuts always find a global optimum for Potts models (with a catch)
On "real-world" instances, MAP assignments of small perturbations of the problem should be very similar to the MAP assignment(s) of the original problem instance.
Learning a mixture of two subspaces over finite fields
We study the problem of learning a mixture of two subspaces over $\mathbb{F}_2^n$.
Data Structures and Algorithms
Beyond Perturbation Stability: LP Recovery Guarantees for MAP Inference on Noisy Stable Instances
Several works have shown that perturbation stable instances of the MAP inference problem in Potts models can be solved exactly using a natural linear programming (LP) relaxation.
Efficient Algorithms for Learning Depth-2 Neural Networks with General ReLU Activations
We present polynomial time and sample efficient algorithms for learning an unknown depth-2 feedforward neural network with general ReLU activations, under mild non-degeneracy assumptions.
Agnostic Learning of General ReLU Activation Using Gradient Descent
We provide a convergence analysis of gradient descent for the problem of agnostically learning a single ReLU function under Gaussian distributions.
Classification Protocols with Minimal Disclosure
We consider multi-party protocols for classification that are motivated by applications such as e-discovery in court proceedings.
Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond
While all of these problems are NP-hard in the worst case, our algorithm solves them in polynomial time for generic subspaces of dimension up to a constant multiple of the maximum possible.
Error-Tolerant E-Discovery Protocols
Our goal is to find a protocol that verifies that the responding party sends almost all responsive documents while minimizing the disclosure of non-responsive documents.
