In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve their goal of making the multivariate distribution of covariates for the control group identical to that of the treated, leaving some (potentially multivariate) functions of the covariates with different means between the two groups. When these "imbalanced" functions influence the non-treatment potential outcome, the conditioning on observed covariates fails, and ATT estimates may be biased. Kernel balancing, introduced here, targets a weaker requirement for unbiased ATT estimation, specifically, that the expected non-treatment potential outcome for the treatment and control groups are equal. The conditional expectation of the non-treatment potential outcome is assumed to fall in the space of functions associated with a choice of kernel, implying a set of basis functions in which this regression surface is linear. Weights are then chosen on the control units such that the treated and control group have equal means on these basis functions. As a result, the expectation of the non-treatment potential outcome must also be equal for the treated and control groups after weighting, allowing unbiased ATT estimation by subsequent difference in means or an outcome model using these weights. Moreover, the weights produced are (1) precisely those that equalize a particular kernel-based approximation of the multivariate distribution of covariates for the treated and control, and (2) equivalent to a form of stabilized inverse propensity score weighting, though it does not require assuming any model of the treatment assignment mechanism. An R package, KBAL, is provided to implement this approach.

We study the convergence of the predictive surface of regression trees and forests. To support our analysis we introduce a notion of adaptive concentration for regression trees. This approach breaks tree training into a model selection phase in which we pick the tree splits, followed by a model fitting phase where we find the best regression model consistent with these splits. We then show that the fitted regression tree concentrates around the optimal predictor with the same splits: as d and n get large, the discrepancy is with high probability bounded on the order of sqrt(log(d) log(n)/k) uniformly over the whole regression surface, where d is the dimension of the feature space, n is the number of training examples, and k is the minimum leaf size for each tree. We also provide rate-matching lower bounds for this adaptive concentration statement. From a practical perspective, our result enables us to prove consistency results for adaptively grown forests in high dimensions, and to carry out valid post-selection inference in the sense of Berk et al. [2013] for subgroups defined by tree leaves.

In this paper we present a method for learning a discriminative classifier from unlabeled or partially labeled data. Our approach is based on an objective function that trades-off mutual information between observed examples and their predicted categorical class distribution, against robustness of the classifier to an adversarial generative model. The resulting algorithm can either be interpreted as a natural generalization of the generative adversarial networks (GAN) framework or as an extension of the regularized information maximization (RIM) framework to robust classification against an optimal adversary. We empirically evaluate our method - which we dub categorical generative adversarial networks (or CatGAN) - on synthetic data as well as on challenging image classification tasks, demonstrating the robustness of the learned classifiers. We further qualitatively assess the fidelity of samples generated by the adversarial generator that is learned alongside the discriminative classifier, and identify links between the CatGAN objective and discriminative clustering algorithms (such as RIM).

There are two fundamental milestones I'd say. The first one is Fisher's Linear Discriminant [1], later generalized by Rao [2] to what we know as Linear Discriminant Analysis (LDA). Essentially, LDA is a linear transformation (or projection) technique, which is mainly used for dimensionality reduction (i.e., the objective is to find the k-dimensional feature subspace that -- linearly -- separates the samples from different classes best. Given the objective to maximize class separability, projecting the 2D dataset below onto "x-axis component," would be a better choice than the "y-axis component." Keep in mind though that LDA is a projection technique; the feature axes of your new feature subspace are (almost certainly) different from your original axes.

Machine learning algorithms are a very large part of machine learning. You have to understand how they work to make any progress in the field. In this post you will discover a 14-part machine learning algorithms mini course that you can follow to finally understand machine learning algorithms. We are going to cover a lot of ground in this course and you are going to have a great time. Machine Learning Algorithms Mini-Course Photo by Jared Tarbell, some rights reserved. Before we get started, let's make sure you are in the right place. This mini-course will take you on a guided tour of machine learning algorithms from foundations and through 10 top techniques.

Are there any great resources that give an in depth proof of the derivative of the softmax when used within the cross-entropy loss function? I've been struggling to fully derive the softmax and looking for some guidance here.

Sparse generalized eigenvalue problem plays a pivotal role in a large family of high-dimensional learning tasks, including sparse Fisher's discriminant analysis, canonical correlation analysis, and sufficient dimension reduction. However, the theory of sparse generalized eigenvalue problem remains largely unexplored. In this paper, we exploit a non-convex optimization perspective to study this problem. In particular, we propose the truncated Rayleigh flow method (Rifle) to estimate the leading generalized eigenvector and show that it converges linearly to a solution with the optimal statistical rate of convergence. Our theory involves two key ingredients: (i) a new analysis of the gradient descent method on non-convex objective functions, as well as (ii) a fine-grained characterization of the evolution of sparsity patterns along the solution path. Thorough numerical studies are provided to back up our theory. Finally, we apply our proposed method in the context of sparse sufficient dimension reduction to two gene expression data sets.

We introduce a new learned descriptor for audio signals which is efficient for event representation. The entries of the descriptor are produced by evaluating a set of regressors on the input signal. The regressors are class-specific and trained using the random regression forests framework. Given an input signal, each regressor estimates the onset and offset positions of the target event. The estimation confidence scores output by a regressor are then used to quantify how the target event aligns with the temporal structure of the corresponding category. Our proposed descriptor has two advantages. First, it is compact, i.e. the dimensionality of the descriptor is equal to the number of event classes. Second, we show that even simple linear classification models, trained on our descriptor, yield better accuracies on audio event classification task than not only the nonlinear baselines but also the state-of-the-art results.

Some people spend weeks, months, even years trying to learn machine learning without any success. They play around with datasets, buy books, compete on Kaggle, but ultimately make little progress. One of the big problems, is that many people just want to "dive in and build something." I admire the ambition of these students, but I absolutely think that the "just build something" method of learning a new subject is vastly overrated. In order to learn a technical subject, it pays off to have a solid understanding of the conceptual framework that underlies that subject.

Data Scientist communities have their own complex jargon; multivariate regression models, Big data engineering, Hadoop, Map Reduce, Deep Learning etc. But, unfortunately businesses do not seem to care about how complex the term is or how impressive the math is! They want the results explained in non-tech terms. While working on Big Data & planning to implement it for the benefit of business, it is very important to explain the insights & valuable knowledge in a way that non-technical business user can actually understand. Here is my recent experience while working on a project for one of the largest food retailers. The goal of this project was how incentivisation would help improve their overall profits.