24,750 research outputs found
Screening Rules for Convex Problems
We propose a new framework for deriving screening rules for convex
optimization problems. Our approach covers a large class of constrained and
penalized optimization formulations, and works in two steps. First, given any
approximate point, the structure of the objective function and the duality gap
is used to gather information on the optimal solution. In the second step, this
information is used to produce screening rules, i.e. safely identifying
unimportant weight variables of the optimal solution. Our general framework
leads to a large variety of useful existing as well as new screening rules for
many applications. For example, we provide new screening rules for general
simplex and -constrained problems, Elastic Net, squared-loss Support
Vector Machines, minimum enclosing ball, as well as structured norm regularized
problems, such as group lasso
An Algorithmic Framework for Computing Validation Performance Bounds by Using Suboptimal Models
Practical model building processes are often time-consuming because many
different models must be trained and validated. In this paper, we introduce a
novel algorithm that can be used for computing the lower and the upper bounds
of model validation errors without actually training the model itself. A key
idea behind our algorithm is using a side information available from a
suboptimal model. If a reasonably good suboptimal model is available, our
algorithm can compute lower and upper bounds of many useful quantities for
making inferences on the unknown target model. We demonstrate the advantage of
our algorithm in the context of model selection for regularized learning
problems
GAP Safe screening rules for sparse multi-task and multi-class models
High dimensional regression benefits from sparsity promoting regularizations.
Screening rules leverage the known sparsity of the solution by ignoring some
variables in the optimization, hence speeding up solvers. When the procedure is
proven not to discard features wrongly the rules are said to be \emph{safe}. In
this paper we derive new safe rules for generalized linear models regularized
with and norms. The rules are based on duality gap
computations and spherical safe regions whose diameters converge to zero. This
allows to discard safely more variables, in particular for low regularization
parameters. The GAP Safe rule can cope with any iterative solver and we
illustrate its performance on coordinate descent for multi-task Lasso, binary
and multinomial logistic regression, demonstrating significant speed ups on all
tested datasets with respect to previous safe rules.Comment: in Proceedings of the 29-th Conference on Neural Information
Processing Systems (NIPS), 201
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