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Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closel...
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closel...
To recover a sparse signal from an underdetermined system, we often solve a constrained`1-norm minimization problem. In many cases, the signal sparsity and the recovery performance can be further impr...
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem.Consequently, the convex nuclear ...
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and ...
Approachability has become a standard tool in analyzing learning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in th...
We consider the unconstrained L2-Lp minimization: find a minimizer of kAx−bk2 2+λkxkp p for given A ∈ Rm×n, b ∈ Rm and parameters λ > 0, p ∈ [0, 1). This problem has been studied extensively...
We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function $T$ and the learning class $F$...
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy ...
We assume data independently sampled froma mixture distribution on the unit ball of RD withK+1 components: the first component is a uniform distribution on that ball representing outliers and the oth...
We study estimation of a multivariate function f :Rd !R when the observations are available from the function Af, where A is a known linear operator. Both the Gaussian white noise model and densit...
Extension of Lipschitz integrands and minimization of nonconvex integral functionals. Applications to the optimal recourse problem in discrete time。
Kernel methods are closely related to the notion of reproducing kernel Hilbert space (RKHS). A kernel machine is based on the minimization of an empirical cost and a stabilizer (usually the norm in th...
The ane rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a divers...
Let F be a set of M classification procedures with values in [−1, 1]. Given a loss function, we want to construct a procedure which mimics at the best possible rate the best procedure in F. Th...

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