Bundle methods for regularized risk minimization
Bundle Methods for Regularized Risk Minimization
... approximation methods such as the Random Feature Map proposed by Rahimi and Recht (2008) can efficiently approximate a infinite dimensional nonlinear feature map associated to a kernel by a finite dimensional ...
55
Bundle methods for regularized risk minimization with applications to robust learning
... In Fifteenth Text HEtrieval Conference (TREC-2006). Cortes and Nainiik. Supi)ort vector networks. Probabilistic Networks and Expert Sytems. Online passive-aggressive algorithms. Advan[r] ...
159
Stochastic Methods for l1-regularized Loss Minimization
... We ran 4 algorithms on these data sets: SCD, GCD, SMIDAS, and T RUNC G RAD . SCD is the stochastic coordinate descent algorithm given in Section 2 above. GCD is the corresponding deter- ministic and “greedy” version of ...
28
Regularized Bundle Methods for Convex and Non-Convex Risks
... on regularized unconstrained optimization problems which cover a large number of modern machine learning problems such as logistic regression, conditional random fields, large margin estimation, ...larized ...
45
The Common-directions Method for Regularized Empirical Risk Minimization
... ∇ 2 f (w)p = −∇f(w) ⇒ p = −∇ 2 f (w) −1 ∇f(w). (36) Then a line search procedure is conducted to ensure the sufficient function decrease. It is known that for twice-differentiable functions satisfying Assumption 2, the ...
49
Stochastic Dual Coordinate Ascent Methods for Regularized Loss Minimization
... In Figure 5 we compare choosing dual variables at random with repetitions (as done in SDCA) vs. choosing dual variables using a random permutation at each epoch (as done in SDCA-Perm) vs. choosing dual variables in a ...
33
Regularized gradient projection methods for equilibrium and constrained convex minimization problems
... the regularized gradient-projection algorithm (RGPA) and the averaged mappings approach is proposed for finding a common solution of equilibrium and constrained convex minimization ...
22
Stochastic Primal-Dual Coordinate Method for Regularized Empirical Risk Minimization
... We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave ...
42
Regularized gradient projection methods for finding the minimum norm solution of the constrained convex minimization problem
... many methods to solve the constrained convex mini- mization ...the regularized gradient-projection algorithm to find the minimum- norm solution of the constrained convex minimization problem, where ...
12
Efficient Methods For Large-Scale Empirical Risk Minimization
... loss minimization suggests that ERM problems have more structure than FSM ...existing methods which, albeit used for ERM, are in fact designed for ...loss minimization to achieve lower overall ...
321
Regularized gradient-projection methods for the constrained convex minimization problem and the zero points of maximal monotone operator
... the regularized gradient-projection algorithm, we find a common element of the solution set of a constrained convex minimization problem and the set of zero points of the maximal monotone operator ...convex ...
23
On robustness properties of convex risk minimization methods for pattern recognition
... Obviously, the proof that many classifiers based on convex loss functions are universally consistent under weak conditions is a strong argument in favor of these statistical learning methods. Nevertheless, it is ...
20
Classification Methods with Reject Option Based on Convex Risk Minimization
... empirical risk minimization easily becomes infeasible, the paper proposes minimizing convex risks based on surrogate convex loss ...excess risk can be bounded through the excess surrogate risk ...
20
On Robustness Properties of Convex Risk Minimization Methods for Pattern Recognition
... learning methods to a data set with a finite sample ...learning methods are nonparametric ...prediction methods and the development of methods such that the impact of such data points is ...
28
Consistency of Multiclass Empirical Risk Minimization Methods Based on Convex Loss
... the underlying distribution D. The goal of statistical learning is to find a classifier based on the samples and a pre-chosen set F of vector functions with K-components. For this purpose, a very successful method used ...
13
A General Distributed Dual Coordinate Optimization Framework for Regularized Loss Minimization
... mini-batch methods to design reasonable aggregation strategies to achieve fast ...second-order methods as special ...descent methods for solving ` 1 regularized loss minimization ...
52
Some Properties of Regularized Kernel Methods
... In regularized kernel methods, the solution of a learning problem is found by minimizing func- tionals consisting of the sum of a data and a complexity ...
28
Asymptotics in Empirical Risk Minimization
... In the statistical theory of classification, rates of convergence of empirical classifiers have been studied by a number of researchers, see for example Lugosi and Vayatis (2004), Lugosi and Nobel (1999), Lugosi and ...
21
Excess risk bounds in robust empirical risk minimization
... This work is devoted to robust algorithms in the framework of statistical learning. A recent Forbes article [ 41 ] states that “Machine learning algorithms are very dependent on accurate, clean, and well- labeled ...
49
Differentially Private Empirical Risk Minimization
... perturbation methods alter the output of the func- tion computed on the database, before releasing it; in particular the sensitivity method makes an algorithm differentially private by adding noise to its ...
41