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Random Features for Large-Scale Kernel Machines
Two sets of random features are explored, provided convergence bounds on their ability to approximate various radial basis kernels, and it is shown that in large-scale classification and regression tasks linear machine learning algorithms applied to these features outperform state-of-the-art large- scale kernel machines.
Exact Matrix Completion via Convex Optimization
It is proved that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries, and that objects other than signals and images can be perfectly reconstructed from very limited information.
Understanding deep learning requires rethinking generalization
- Chiyuan Zhang, Samy Bengio, Moritz Hardt, B. Recht, Oriol Vinyals
- Computer ScienceICLR
- 4 November 2016
These experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data, and confirm that simple depth two neural networks already have perfect finite sample expressivity.
Hogwild: A Lock-Free Approach to Parallelizing Stochastic Gradient Descent
This work aims to show using novel theoretical analysis, algorithms, and implementation that SGD can be implemented without any locking, and presents an update scheme called HOGWILD! which allows processors access to shared memory with the possibility of overwriting each other's work.
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
It is shown that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum-rank solution can be recovered by solving a convex optimization problem, namely, the minimization of the nuclear norm over the given affine space.
The Convex Geometry of Linear Inverse Problems
- V. Chandrasekaran, B. Recht, P. Parrilo, A. Willsky
- Computer ScienceFound. Comput. Math.
- 3 December 2010
This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems.
Train faster, generalize better: Stability of stochastic gradient descent
We show that parametric models trained by a stochastic gradient method (SGM) with few iterations have vanishing generalization error. We prove our results by arguing that SGM is algorithmically…
Compressed Sensing Off the Grid
- Gongguo Tang, Badri Narayan Bhaskar, P. Shah, B. Recht
- MathematicsIEEE Transactions on Information Theory
- 25 July 2012
This paper investigates the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples and proposes an atomic norm minimization approach to exactly recover the unobserved samples and identify the unknown frequencies.
A Simpler Approach to Matrix Completion
- B. Recht
- Computer ScienceJ. Mach. Learn. Res.
- 5 October 2009
This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low-rank matrix by minimizing the nuclear norm of the hidden matrix subject to agreement with the provided entries.
Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints
A new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory is developed, proving new inequalities about convex functions and providing a version of IQC theory adapted for use by optimization researchers.