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Found 38 papers, 2 papers with code
On Human-Aligned Risk Minimization
The statistical decision theoretic foundations of modern machine learning have largely focused on the minimization of the expectation of some loss function for a given task.
On the (In)fidelity and Sensitivity of Explanations
We analyze optimal explanations with respect to both these measures, and while the optimal explanation for sensitivity is a vacuous constant explanation, the optimal explanation for infidelity is a novel combination of two popular explanation methods.
Optimal Analysis of Subset-Selection Based L_p Low-Rank Approximation
We show that this algorithm has an approximation ratio of $O((k+1)^{1/p})$ for $1\le p\le 2$ and $O((k+1)^{1-1/p})$ for $p\ge 2$.
MixLasso: Generalized Mixed Regression via Convex Atomic-Norm Regularization
We consider a generalization of mixed regression where the response is an additive combination of several mixture components.
The Sample Complexity of Semi-Supervised Learning with Nonparametric Mixture Models
We study the sample complexity of semi-supervised learning (SSL) and introduce new assumptions based on the mismatch between a mixture model learned from unlabeled data and the true mixture model induced by the (unknown) class conditional distributions.
Connecting Optimization and Regularization Paths
We study the implicit regularization properties of optimization techniques by explicitly connecting their optimization paths to the regularization paths of ``corresponding'' regularized problems.
The Expxorcist: Nonparametric Graphical Models Via Conditional Exponential Densities
Non-parametric multivariate density estimation faces strong statistical and computational bottlenecks, and the more practical approaches impose near-parametric assumptions on the form of the density functions.
On Separability of Loss Functions, and Revisiting Discriminative Vs Generative Models
We revisit the classical analysis of generative vs discriminative models for general exponential families, and high-dimensional settings.
Dual Decomposed Learning with Factorwise Oracle for Structural SVM of Large Output Domain
In this work, we show that, by decomposing training of Structural Support Vector Machine (SVM) into a series of multiclass SVM problems connected through messages, one can replace expensive structured oracle with Factorwise Maximization Oracle (FMO) that allows efficient implementation of complexity sublinear to the factor domain.
Consistent Multilabel Classification
In particular, we show that for multilabel metrics constructed as instance-, micro- and macro-averages, the population optimal classifier can be decomposed into binary classifiers based on the marginal instance-conditional distribution of each label, with a weak association between labels via the threshold.
Fast Classification Rates for High-dimensional Gaussian Generative Models
We consider the problem of binary classification when the covariates conditioned on the each of the response values follow multivariate Gaussian distributions.
Sparse Linear Programming via Primal and Dual Augmented Coordinate Descent
Over the past decades, Linear Programming (LP) has been widely used in different areas and considered as one of the mature technologies in numerical optimization.
Fixed-Length Poisson MRF: Adding Dependencies to the Multinomial
We show the effectiveness of our LPMRF distribution over Multinomial models by evaluating the test set perplexity on a dataset of abstracts and Wikipedia.
Beyond Sub-Gaussian Measurements: High-Dimensional Structured Estimation with Sub-Exponential Designs
In contrast, for the sub-exponential setting, we show that the sample complexity and the estimation error will depend on the exponential width of the corresponding sets, and the analysis holds for any norm.
Closed-form Estimators for High-dimensional Generalized Linear Models
We propose a class of closed-form estimators for GLMs under high-dimensional sampling regimes.
Collaborative Filtering with Graph Information: Consistency and Scalable Methods
Low rank matrix completion plays a fundamental role in collaborative filtering applications, the key idea being that the variables lie in a smaller subspace than the ambient space.
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QUIC & DIRTY: A Quadratic Approximation Approach for Dirty Statistical Models
In this paper, we develop a family of algorithms for optimizing superposition-structured” or “dirty” statistical estimators for high-dimensional problems involving the minimization of the sum of a smooth loss function with a hybrid regularization.
Capturing Semantically Meaningful Word Dependencies with an Admixture of Poisson MRFs
We develop a fast algorithm for the Admixture of Poisson MRFs (APM) topic model and propose a novel metric to directly evaluate this model.
A Representation Theory for Ranking Functions
This paper presents a representation theory for permutation-valued functions, which in their general form can also be called listwise ranking functions.
Constant Nullspace Strong Convexity and Fast Convergence of Proximal Methods under High-Dimensional Settings
State of the art statistical estimators for high-dimensional problems take the form of regularized, and hence non-smooth, convex programs.
Elementary Estimators for Graphical Models
We propose a class of closed-form estimators for sparsity-structured graphical models, expressed as exponential family distributions, under high-dimensional settings.
Consistent Binary Classification with Generalized Performance Metrics
We consider a fairly large family of performance metrics given by ratios of linear combinations of the four fundamental population quantities.
Sparse Random Feature Algorithm as Coordinate Descent in Hilbert Space
In this paper, we propose a Sparse Random Feature algorithm, which learns a sparse non-linear predictor by minimizing an $\ell_1$-regularized objective function over the Hilbert Space induced from kernel function.
Dirty Statistical Models
We provide a unified framework for the high-dimensional analysis of “superposition-structured” or “dirty” statistical models: where the model parameters are a “superposition” of structurally constrained parameters.
Conditional Random Fields via Univariate Exponential Families
We thus introduce a “novel subclass of CRFs”, derived by imposing node-wise conditional distributions of response variables conditioned on the rest of the responses and the covariates as arising from univariate exponential families.
BIG & QUIC: Sparse Inverse Covariance Estimation for a Million Variables
The l1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix even under high-dimensional settings.
Learning with Noisy Labels
In this paper, we theoretically study the problem of binary classification in the presence of random classification noise --- the learner, instead of seeing the true labels, sees labels that have independently been flipped with some small probability.
On Poisson Graphical Models
Undirected graphical models, such as Gaussian graphical models, Ising, and multinomial/categorical graphical models, are widely used in a variety of applications for modeling distributions over a large number of variables.
Large Scale Distributed Sparse Precision Estimation
We consider the problem of sparse precision matrix estimation in high dimensions using the CLIME estimator, which has several desirable theoretical properties.
Graphical Models via Generalized Linear Models
Our models allow one to estimate networks for a wide class of exponential distributions, such as the Poisson, negative binomial, and exponential, by fitting penalized GLMs to select the neighborhood for each node.
A Divide-and-Conquer Method for Sparse Inverse Covariance Estimation
We derive a bound on the distance of the approximate solution to the true solution.
On Learning Discrete Graphical Models using Greedy Methods
In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting.
Nearest Neighbor based Greedy Coordinate Descent
In particular, we investigate the greedy coordinate descent algorithm, and note that performing the greedy step efficiently weakens the costly dependence on the problem size provided the solution is sparse.
Greedy Algorithms for Structurally Constrained High Dimensional Problems
A hallmark of modern machine learning is its ability to deal with high dimensional problems by exploiting structural assumptions that limit the degrees of freedom in the underlying model.
A Dirty Model for Multi-task Learning
However, these papers also caution that the performance of such block-regularized methods are very dependent on the {\em extent} to which the features are shared across tasks.
Information-theoretic lower bounds on the oracle complexity of convex optimization
The extensive use of convex optimization in machine learning and statistics makes such an understanding critical to understand fundamental computational limits of learning and estimation.
A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers
The estimation of high-dimensional parametric models requires imposing some structure on the models, for instance that they be sparse, or that matrix structured parameters have low rank.
Nonparametric sparse hierarchical models describe V1 fMRI responses to natural images
We propose a novel hierarchical, nonlinear model that predicts brain activity in area V1 evoked by natural images.
