Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Rate-optimal procedures such as Tukey's median and other estimators based on statistical depth functions are impractical because of their computational intractability. In this paper, we establish an intriguing connection between f-GANs and various depth functions through the lens of f-Learning. Similar to the derivation of f-GAN, we show that these depth functions that lead to rate-optimal robust estimators can all be viewed as variational lower bounds of the total variation distance in the framework of f-Learning. This connection opens the door of computing robust estimators using tools developed for training GANs. In particular, we show that a JS-GAN that uses a neural network discriminator with at least one hidden layer is able to achieve the minimax rate of robust mean estimation under Huber's $\epsilon$-contamination model. Interestingly, the hidden layers for the neural net structure in the discriminator class is shown to be necessary for robust estimation.

One of the definitional debates that bedevils the artificial intelligence (AI) field is whether machine learning is an AI-based method or technology. Or is it just an analytics-based activity? After all, it is statistical in nature, and attempts--as virtually analytical methods do--to fit a line or curve to a set of data points. And what difference does it make? Basic machine learning is practically indistinguishable from predictive analytics.

The difference between regression machine learning algorithms and classification machine learning algorithms sometimes confuse most data scientists, which make them to implement wrong methodologies in solving their prediction problems. Andreybu, who is from Germany and has more than 5 years of machine learning experience, says that "understanding whether the machine learning task is a regression or classification problem is key for selecting the right algorithm to use." Let's start by talking about the similarities between the two techniques. Regression and classification are categorized under the same umbrella of supervised machine learning. Both share the same concept of utilizing known datasets (referred to as training datasets) to make predictions. In supervised learning, an algorithm is employed to learn the mapping function from the input variable (x) to the output variable (y); that is y f(X).

This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach: first, construct a possibly non-sparse model that predicts well, and then find a minimal subset of features that characterize the predictions. The model built in the first step is referred to as the \emph{reference model} and the operation during the latter step as predictive \emph{projection}. The key characteristic of this approach is that it finds an excellent tradeoff between sparsity and predictive accuracy, and the gain comes from utilizing all available information including prior and that coming from the left out features. We review several methods that follow this principle and provide novel methodological contributions. We present a new projection technique that unifies two existing techniques and is both accurate and fast to compute. We also propose a way of evaluating the feature selection process using fast leave-one-out cross-validation that allows for easy and intuitive model size selection. Furthermore, we prove a theorem that helps to understand the conditions under which the projective approach could be beneficial. The benefits are illustrated via several simulated and real world examples.

However, some seasoned techniques are here to stay. At the top of the list are regression techniques. As long as this number is as high, you will encounter regressions during your machine learning career. Even if you don't use them yourself, it is essential to be aware of the different flavors and which problems they tackle. In this post, I provide you with a quick overview of five different (groups of) regressions.

We obtain the first positive results for bounded sample compression in the agnostic regression setting. We show that for p in {1,infinity}, agnostic linear regression with $\ell_p$ loss admits a bounded sample compression scheme. Specifically, we exhibit efficient sample compression schemes for agnostic linear regression in $R^d$ of size $d+1$ under the $\ell_1$ loss and size $d+2$ under the $\ell_\infty$ loss. We further show that for every other $\ell_p$ loss (1 < p < infinity), there does not exist an agnostic compression scheme of bounded size. This refines and generalizes a negative result of David, Moran, and Yehudayoff (2016) for the $\ell_2$ loss. We close by posing a general open question: for agnostic regression with $\ell_1$ loss, does every function class admit a compression scheme of size equal to its pseudo-dimension? This question generalizes Warmuth's classic sample compression conjecture for realizable-case classification (Warmuth, 2003).

We used Python's Flask framework for building the service and exposed a REST API that generates a bias report based on the following input parameters from a user: the dataset name, the protected attributes, the privileged and unprivileged groups, the chosen fairness metrics, and the chosen mitigation algorithm, if any. With these inputs, the back-end then runs a series of steps to 1) split the dataset into training, development, and validation sets; 2) train a logistic regression classifier on the training set; 3) run the bias-checking metrics on the classifier against the test dataset; 4) if a mitigation algorithm is chosen, run the mitigation algorithm with the appropriate pipeline (pre-processing, in-processing, or post-processing). The end result is then cached so that if the exact same inputs are provided, the result can be directly retrieved from cache and no additional computation is needed. The reason to truly use the toolkit code in serving the Web application rather than having a pre-computed lookup table of results is twofold: we want to make the app a real representation of the underlying capabilities (in fact, creating the Web app helped us debug a few items in the code), and we also avoid any issues of synchronizing updates to the metrics, explainers, and algorithms with the results shown: synchronization is automatic. Currently, the service is limited to three built-in datasets, but it can be expanded to support the user's own data upload. The service is also limited to building logistic regression classifiers, but again this can be expanded. Such expansions can be more easily implemented if this fairness service is integrated into a full AI suite that provides various classifier options and data storage solutions.

Search queries are appropriate when users have explicit intent, but they perform poorly when the intent is difficult to express or if the user is simply looking to be inspired. Visual browsing systems allow e-commerce platforms to address these scenarios while offering the user an engaging shopping experience. Here we explore extensions in the direction of adaptive personalization and item diversification within Stream, a new form of visual browsing and discovery by Amazon. Our system presents the user with a diverse set of interesting items while adapting to user interactions. Our solution consists of three components (1) a Bayesian regression model for scoring the relevance of items while leveraging uncertainty, (2) a submodular diversification framework that re-ranks the top scoring items based on category, and (3) personalized category preferences learned from the user's behavior. When tested on live traffic, our algorithms show a strong lift in click-through-rate and session duration.

Many state-of-the-art machine learning models such as deep neural networks have recently shown to be vulnerable to adversarial perturbations, especially in classification tasks. Motivated by adversarial machine learning, in this paper we investigate the robustness of sparse regression models with strongly correlated covariates to adversarially designed measurement noises. Specifically, we consider the family of ordered weighted $\ell_1$ (OWL) regularized regression methods and study the case of OSCAR (octagonal shrinkage clustering algorithm for regression) in the adversarial setting. Under a norm-bounded threat model, we formulate the process of finding a maximally disruptive noise for OWL-regularized regression as an optimization problem and illustrate the steps towards finding such a noise in the case of OSCAR. Experimental results demonstrate that the regression performance of grouping strongly correlated features can be severely degraded under our adversarial setting, even when the noise budget is significantly smaller than the ground-truth signals.

Enormous online textual information provides intriguing opportunities for understandings of social and economic semantics. In this paper, we propose a novel text regression model based on a conditional generative adversarial network (GAN), with an attempt to associate textual data and social outcomes in a semi-supervised manner. Besides promising potential of predicting capabilities, our superiorities are twofold: (i) the model works with unbalanced datasets of limited labelled data, which align with real-world scenarios; and (ii) predictions are obtained by an end-to-end framework, without explicitly selecting high-level representations. Finally we point out related datasets for experiments and future research directions.