When you want to purchase a new car, will you walk up to the first car shop and purchase one based on the advice of the dealer? You would likely browser a few web portals where people have posted their reviews and compare different car models, checking for their features and prices. You will also probably ask your friends and colleagues for their opinion. In short, you wouldn't directly reach a conclusion, but will instead make a decision considering the opinions of other people as well. Ensemble models in machine learning operate on a similar idea. They combine the decisions from multiple models to improve the overall performance.

Predictive analytics in data science rest on the shoulders of explanatory data analysis, which is precisely what we were discussing in our previous article – The What, Where and How of Data for Data Science. We talked about data in data science, and how business intelligence (BI) analysts use it to explain the past. In fact, everything is connected. Once the BI reports and dashboards have been prepared and insights – extracted from them – this information becomes the basis for predicting future values. And the accuracy of these predictions lies in the methods used.

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with conventional stochastic variance reduced gradient (SVRG) algorithm that uses two reference points to construct a semi-stochastic gradient with diminishing variance in each iteration, our algorithm uses $K+1$ nested reference points to build a semi-stochastic gradient to further reduce its variance in each iteration. For smooth nonconvex functions, the proposed algorithm converges to an $\epsilon$-approximate first-order stationary point (i.e., $\|\nabla F(\mathbf{x})\|_2\leq \epsilon$) within $\tilde{O}(n\land \epsilon^{-2}+\epsilon^{-3}\land n^{1/2}\epsilon^{-2})$ number of stochastic gradient evaluations. This improves the best known gradient complexity of SVRG $O(n+n^{2/3}\epsilon^{-2})$ and that of SCSG $O(n\land \epsilon^{-2}+\epsilon^{-10/3}\land n^{2/3}\epsilon^{-2})$. For gradient dominated functions, our algorithm also achieves a better gradient complexity than the state-of-the-art algorithms.

Online social media platforms generally attempt to mitigate hateful expressions, as these comments can be detrimental to the health of the community. However, automatically identifying hateful comments can be challenging. We manually label 5,143 hateful expressions posted to YouTube and Facebook videos among a dataset of 137,098 comments from an online news media. We then create a granular taxonomy of different types and targets of online hate and train machine learning models to automatically detect and classify the hateful comments in the full dataset. Our contribution is twofold: 1) creating a granular taxonomy for hateful online comments that includes both types and targets of hateful comments, and 2) experimenting with machine learning, including Logistic Regression, Decision Tree, Random Forest, Adaboost, and Linear SVM, to generate a multiclass, multilabel classification model that automatically detects and categorizes hateful comments in the context of online news media. We find that the best performing model is Linear SVM, with an average F1 score of 0.79 using TF-IDF features. We validate the model by testing its predictive ability, and, relatedly, provide insights on distinct types of hate speech taking place on social media.

We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher network. We analyze the performance of gradient descent for training such kind of neural networks based on empirical risk minimization, and provide algorithm-dependent guarantees. In particular, we prove that tensor initialization followed by gradient descent can converge to the ground-truth parameters at a linear rate up to some statistical error. To the best of our knowledge, this is the first work characterizing the recovery guarantee for practical learning of one-hidden-layer ReLU networks with multiple neurons. Numerical experiments verify our theoretical findings.

Computable Stein discrepancies have been deployed for a variety of applications, including sampler selection in posterior inference, approximate Bayesian inference, and goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational cost that grows quadratically in the sample size. While linear-time Stein discrepancies have been proposed for goodness-of-fit testing, they exhibit avoidable degradations in testing power---even when power is explicitly optimized. To address these shortcomings, we introduce feature Stein discrepancies ($\Phi$SDs), a new family of quality measures that can be cheaply approximated using importance sampling. We show how to construct $\Phi$SDs that provably determine the convergence of a sample to its target and develop high-accuracy approximations---random $\Phi$SDs (R$\Phi$SDs)---which are computable in near-linear time. In our experiments with sampler selection for approximate posterior inference and goodness-of-fit testing, R$\Phi$SDs typically perform as well or better than quadratic-time KSDs while being orders of magnitude faster to compute.

Machine learning models (e.g., speech recognizers) are usually trained to minimize average loss, which results in representation disparity---minority groups (e.g., non-native speakers) contribute less to the training objective and thus tend to suffer higher loss. Worse, as model accuracy affects user retention, a minority group can shrink over time. In this paper, we first show that the status quo of empirical risk minimization (ERM) amplifies representation disparity over time, which can even make initially fair models unfair. To mitigate this, we develop an approach based on distributionally robust optimization (DRO), which minimizes the worst case risk over all distributions close to the empirical distribution. We prove that this approach controls the risk of the minority group at each time step, in the spirit of Rawlsian distributive justice, while remaining oblivious to the identity of the groups. We demonstrate that DRO prevents disparity amplification on examples where ERM fails, and show improvements in minority group user satisfaction in a real-world text autocomplete task.

Motivation Deep neural networks have found success in a wide range of machine learning applications. However, despite significant empirical success, a rigorous algorithmic understanding of training such networks remains far less well understood. Our focus in this paper are on a class of neural networks with rectified linear units (ReLUs) as activation functions. The method of choice to train such networks is the popular (stochastic) gradient descent. ReLU networks are computationally less expensive to train when compared to networks with tanh or sigmoid activations since they generally involve simpler gradient update steps. Due to their utility as well as amenability to analysis, several recent papers have addressed the problem of provably showing that gradient descent for ReLU networks succeeds under various assumptions [1, 2, 3, 4] Our contributions In this paper, we depart from the standard approach of gradient descent for learning ReLUbased neural networks. Instead, we propose a new approach based on the technique of alternating minimization. In contrast with gradient-based learning, our algorithm is parameter-free: it does not involve any tuning parameters (such as learning rate, damping factor, dropout ratio, etc.) other than setting the number of training epochs. To the best of our knowledge, such an alternating minimization approach in the context of neural network learning is novel.

The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not yet been well-established for regression tasks. This paper considers the problem of calibrating a probabilistic regression model to improve the estimated probability densities over the real-valued targets. We propose to calibrate a regression model through the cumulative probability density, which can be derived from calibrating a multi-class classifier. We provide three non-parametric approaches to solve the problem, two of which provide empirical estimates and the third providing smooth density estimates. The proposed approaches are experimentally evaluated to show their ability to improve the performance of regression models on the predictive likelihood.

Many estimators of the average causal effect of an intervention require estimation of the propensity score, the outcome regression, or both. For these estimators, we must carefully con- sider how to estimate the relevant regressions. It is often beneficial to utilize flexible techniques such as semiparametric regression or machine learning. However, optimal estimation of the regression function does not necessarily lead to optimal estimation of the average causal effect. Therefore, it is important to consider criteria for evaluating regression estimators and selecting hyper-parameters. A recent proposal addressed these issues via the outcome-adaptive lasso, a penalized regression technique for estimating the propensity score. We build on this proposal and offer a method that is simultaneously more flexible and more efficient than the previous pro- posal. We propose the outcome-highly-adaptive LASSO, a semi-parametric regression estimator designed to down-weight regions of the confounder space that do not contribute variation to the outcome regression. We show that tuning this method using collaborative targeted learning leads to superior finite-sample performance relative to competing estimators.