Paper separator machine

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Paper separator machine

Abstract We show that the stochastic gradient descent algorithm provides an implicit regularization effect in the learning of over-parameterized matrix factorization models and one-hidden-layer neural networks with quadratic activations. The results Paper separator machine the conjecture of Gunasekar et al.

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The technique can be applied to analyzing neural networks with quadratic activations with some technical modifications. Abstract Recently, research in unsupervised learning has gravitated towards exploring statistical-computational gaps induced by sparsity. However, the delicate nature of average-case reductions has limited the development of techniques and often led to weaker hardness results that only apply to algorithms robust to different noise distributions or that do not need to know the parameters of the problem.

We introduce several new techniques to give a web of average-case reductions showing strong computational lower bounds based on the planted clique conjecture. Our new lower bounds include: We show that sparse rank-1 submatrix detection is often harder than biclustering, and obtain two different tight lower bounds for these problems with different reductions from planted clique.

This yields the first tight characterization of a computational barrier for sparse PCA over an entire parameter regime. We demonstrate a subtlety in the complexity of sparse PCA and planted dense subgraph by introducing two variants of these problems, biased sparse PCA and planted stochastic block model, and showing that they have different hard regimes than the originals.

Paper separator machine

Our results demonstrate that, despite the delicate nature of average-case reductions, using natural problems as intermediates can often be beneficial, as is the case for reductions between deterministic problems.

Our main technical contribution is to introduce a set of cloning techniques that maintain the level of signal in an instance of a problem while increasing the size of its planted structure.

We also give algorithms matching our lower bounds and identify the information-theoretic limits of the models we introduce. Abstract Learning linear predictors with the logistic loss both in stochastic and online settings is a fundamental task in learning and statistics, with direct connections to classification and boosting.

Existing "fast rates" for this setting exhibit exponential dependence on the predictor norm, and Hazan et al. This provides a positive resolution to a variant of the COLT open problem of mcmahanopen when improper learning is allowed.

This improvement is obtained both in the online setting and, with some extra work, in the batch statistical setting with high probability. We show that the improved dependency on predictor norm is also near-optimal.

Leveraging this improved dependency on the predictor norm also yields the following applications: Finally, we give information-theoretic bounds on the optimal rates for improper logistic regression with general function classes, thereby characterizing the extent to which our improvement for linear classes extends to other parameteric or even nonparametric classes.

The best student paper awards are sponsored by the Mark Fulk Foundation and: Abstract A generative model may generate utter nonsense when it is fit to maximize the likelihood of observed data. To address this, we propose a model of active distribution learning using a binary invalidity oracle that identifies some examples as clearly invalid, together with random positive examples sampled from the true distribution.the Barista Express Espresso Machine by Breville Everything you need for barista quality coffee, in a compact footprint.

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Paper separator machine

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