In this paper, we consider stochastic dual coordinate (SDCA) {\em without} strongly convex assumption or convex assumption. We show that SDCA converges linearly under mild conditions termed restricted strong convexity. This covers a wide array of popular statistical models including Lasso, group Lasso, and logistic regression with $\ell_1$ regularization, corrected Lasso and linear regression with SCAD regularizer. This significantly improves previous convergence results on SDCA for problems that are not strongly convex. As a by product, we derive a dual free form of SDCA that can handle general regularization term, which is of interest by itself.

While there's not necessarily a "correct" answer here, it's most likely you split the bugs into four clusters. That wasn't too bad, was it? You could probably do the same with twice as many bugs, right? If you had a bit of time to spare -- or a passion for entomology -- you could probably even do the same with a hundred bugs. For a machine though, grouping ten objects into however many meaningful clusters is no small task, thanks to a mind-bending branch of maths called combinatorics, which tells us that are 115,975 different possible ways you could have grouped those ten insects together. Had there been twenty bugs, there would have been over fifty trillion possible ways of clustering them. With a hundred bugs -- there'd be many times more solutions than there are particles in the known universe. In fact, there are more than four million billion googol solutions (what's a googol?).

Quick question I guess, but is there a perceivable difference between the terms Statistical Learning and Machine Learning, or is it simply area jargon? I gather the computer scientists like to refer to machine learning while statisticians might refer to statistical learning (no less influenced by the famous book). This motif repeats across other questions in the site as well, with many questions like "what's the difference between machine learning and something else", but I'd like to have this one specifically answered (with some references if possible) to solve the possible merge of the terms. This question is rooted in a recent question on meta regarding The *learning tags, where SL and ML were agreed to be made synonyms (refer to my answer for some background and what I have gathered on the subject so far). Perphaps the difference is simply cultural, like many discussions in the main site pointed.

Since the events of the Arab Spring, there has been increased interest in using social media to anticipate social unrest. While efforts have been made toward automated unrest prediction, we focus on filtering the vast volume of tweets to identify tweets relevant to unrest, which can be provided to downstream users for further analysis. We train a supervised classifier that is able to label Arabic language tweets as relevant to unrest with high reliability. We examine the relationship between training data size and performance and investigate ways to optimize the model building process while minimizing cost. We also explore how confidence thresholds can be set to achieve desired levels of performance.

We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k growing appropriately with sample size. We will argue that a margin-regularized 1-NN enjoys considerable statistical and algorithmic advantages over the k-NN classifier. These include user-friendly finite-sample error bounds, as well as time- and memory-efficient learning and test-point evaluation algorithms with a principled speed-accuracy tradeoff. Encouraging empirical results are reported.

The intersection of causal inference and machine learning is a rapidly advancing field. We propose a new approach, the method of direct estimation, that draws on both traditions in order to obtain nonparametric estimates of treatment effects. The approach focuses on estimating the effect of fluctuations in a treatment variable on an outcome. A tensor-spline implementation enables rich interactions between functional bases allowing for the approach to capture treatment/covariate interactions. We show how new innovations in Bayesian sparse modeling readily handle the proposed framework, and then document its performance in simulation and applied examples. Furthermore we show how the method of direct estimation can easily extend to structural estimators commonly used in a variety of disciplines, like instrumental variables, mediation analysis, and sequential g-estimation.

Implicit discourse relation classification is of great challenge due to the lack of connectives as strong linguistic cues, which motivates the use of annotated implicit connectives to improve the recognition. We propose a feature imitation framework in which an implicit relation network is driven to learn from another neural network with access to connectives, and thus encouraged to extract similarly salient features for accurate classification. We develop an adversarial model to enable an adaptive imitation scheme through competition between the implicit network and a rival feature discriminator. Our method effectively transfers discriminability of connectives to the implicit features, and achieves state-of-the-art performance on the PDTB benchmark.

I watched Ilya Sutskever's talk on their new evolutionary strategies paper. The reason this paper is fascinating is that they use a relatively dumb, simple stochastic method of optimisation that shouldn't really work well in practice, and show that it is actually competitive with SGD/back-propagation-based methods in RL. This is mainly due to the fact that it parallelizes so naturally. Evolution strategies (ES) is can be best described as a gradient descent method which uses gradients estimated from stochastic perturbations around the current parameter value. While the authors did comparisons in the context of RL, and there are many RL-specific advantages, here I'm focussing on ES as a general black-box optimisation method.

Suppose that we observe $y \in \mathbb{R}^n$ and $X \in \mathbb{R}^{n \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* +\epsilon \\ X & = & X_0 + W, \end{eqnarray*} where $X_0$ is an $n \times m$ design matrix with independent subgaussian row vectors, $\epsilon \in \mathbb{R}^n$ is a noise vector and $W$ is a mean zero $n \times m$ random noise matrix with independent subgaussian column vectors, independent of $X_0$ and $\epsilon$. This model is significantly different from those analyzed in the literature in the sense that we allow the measurement error for each covariate to be a dependent vector across its $n$ observations. Such error structures appear in the science literature when modeling the trial-to-trial fluctuations in response strength shared across a set of neurons. Under sparsity and restrictive eigenvalue type of conditions, we show that one is able to recover a sparse vector $\beta^* \in \mathbb{R}^m$ from the model given a single observation matrix $X$ and the response vector $y$. We establish consistency in estimating $\beta^*$ and obtain the rates of convergence in the $\ell_q$ norm, where $q = 1, 2$. We show error bounds which approach that of the regular Lasso and the Dantzig selector in case the errors in $W$ are tending to 0. We analyze the convergence rates of the gradient descent methods for solving the nonconvex programs and show that the composite gradient descent algorithm is guaranteed to converge at a geometric rate to a neighborhood of the global minimizers: the size of the neighborhood is bounded by the statistical error in the $\ell_2$ norm. Our analysis reveals interesting connections between computational and statistical efficiency and the concentration of measure phenomenon in random matrix theory. We provide simulation evidence illuminating the theoretical predictions.

Person recognition aims at recognizing the same identity across time and space with complicated scenes and similar appearance. In this paper, we propose a novel method to address this task by training a network to obtain robust and representative features. The intuition is that we directly compare and optimize the cosine distance between two features - enlarging inter-class distinction as well as alleviating inner-class variance. We propose a congenerous cosine loss by minimizing the cosine distance between samples and their cluster centroid in a cooperative way. Such a design reduces the complexity and could be implemented via softmax with normalized inputs. Our method also differs from previous work in person recognition that we do not conduct a second training on the test subset. The identity of a person is determined by measuring the similarity from several body regions in the reference set. Experimental results show that the proposed approach achieves better classification accuracy against previous state-of-the-arts.