Sparse multinomial logistic regression: fast algorithms and generalization bounds

By Balaji Krishnapuram, Lawrence Carin, Mário A. T. Figueiredo, Alexander J. Hartemink. 2005

957 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Sparse Partially Linear Additive Models (2014, methodology): “j;1=t0 j gand = minfC j;1=t0 j g. Thus, according to Theorem 2 in [37], Algorithm 1 converges Q-linearly. A.4 Practical Issues A.4.1 Active Set Strategy We employ the widely used active set strategy [39, 40, 41]. After a complete cycle through all the variables, we iterate only on the active set til”
Regularization Paths for Generalized Linear Models via Coordinate Descent (2010, methodology): “Several other researchers have also re-discovered coordinate descent, many for solving the same problems we address in this paper—notably Shevade and Keerthi (2003), Krishnapuram and Hartemink (2005), Genkin et al. (2007) and Wu et al. (2009).”
Optimization with Sparsity-Inducing Penalties (2011, background): “Variants of coordinate descent algorithms have also been considered by [49], by [66], by [128].”
Automated Algorithm Selection: Survey and Perspectives (2018, methodology): “…While the former used empirical hardness models (Leyton-Brown et al., 2002) based on ridge regression (see, e.g., Bishop, 2006), the latter employed hierarchical hardness models (Xu et al., 2007), more precisely sparse multinomial logistic regression (SMLR, see, e.g., Krishnapuram et al., 2005).”
Sparse estimation automatically selects voxels relevant for the decoding of fMRI activity patterns (2008, neutral): “Two different algorithms based on this approach have been proposed for the logistic regression model with the ARD model (Tipping and Faul, 2003) and for the multinomial logistic regression with the Laplace prior (Krishnapuram et al., 2005).”
Hyperspectral image classification via kernel sparse representation (2011, methodology): “A fast algorithm for sparse multinomial logistic regressio n has been developed [11] and successfully”
Sparse Representation for Computer Vision and Pattern Recognition (2010, background): “, [17], [20], [30], have been developed in recent years, leading to state-ofthe-art results in many signal and image processing tasks [11], [32], [44], [48], [51], [54].”
SATzilla: Portfolio-based Algorithm Selection for SAT (2008, methodology): “After eliminating some features that had the same value across all instances and some that were too unstable given only 1 CPU second of local search probing, we ended up using the 48 raw features summarized in Figure 2.”
On Learning Discrete Graphical Models using Group-Sparse Regularization (2011, neutral): “The conditional distribution of Xr given the other variables X\r = {Xt | t ∈ V \{r}} takes the form PΘ∗ [ Xr = j | X\r = x\r ] = exp ( θ∗r;j + ∑ t∈V \{r} ∑ k θ ∗ rt;jkI[xt = k] ) 1 + ∑ ℓ exp ( θ∗r;ℓ + ∑ t∈V \{r} ∑ k θ ∗ rt;ℓkI[xt = k] ) , (5) for all j ∈ {1, . . . ,m− 1}.”
Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors (2012, methodology): “In the context of penalized logistic regression, this approach was proposed by Krishnapuram et al. (2005), who referred to it as a bound optimization algorithm .”
A Comparison of Optimization Methods and Software for Large-scale L1-regularized Linear Classification (2010, background): “Many studies have considered Expectation Maximization (EM) frameworks to solve (1) with logistic loss (e.g., Figueiredo, 2003; Krishnapuram et al., 2004, 2005).”
Variable selection and sensitivity analysis using dynamic trees, with an application to computer code performance tuning (2011, methodology): ““b”) and maximum a posteriori (“map”) estimators via Gibbs sampling (Gramacy and Polson, 2012), an estimator from the glmnet package (“glmn”; Friedman et al., 2010), and the EM-based method (“krish”; Krishnapuram et al., 2005). Results for these comparators on an interaction-expanded set of approxim”