Wine has incredible diversity; there exist over 10,000 different varieties of wine grapes worldwide, and each can be processed in a hundred thousand unique ways. Sommeliers-- those who dedicate their lives to the art of wine tasting-- work to craft flavor profiles for the wines they are given to analyze, using their extensive experience to provide nuanced evaluations of countless bottles of wine every year. But the majority of people have neither the time nor the money to try a variety of wines and develop their palate. Typically, the only claim one can make about a given glass of wine is whether or not it was enjoyable, and without the ability to identify ones taste preferences in wine, it is incredibly difficult for one to discover new wine, and nearly impossible to find wine that directly matches their individual flavor profile. We hope to develop an algorithm to address both of these issues, becoming a personal sommelier for the user. Our algorithm takes a history of the wine a user has tasted as input, and returns a set of optimal wines for the user to try next, as well as a description of the flavor profile that inspired the recommendations. Thus, the algorithm could become an avenue for the user to confidently explore wine, and understand more quickly what they do and do not like in wine. Formally, we define our problem as an unsupervised learning problem.

Classifiers can be trained with data-dependent constraints to satisfy fairness goals, reduce churn, achieve a targeted false positive rate, or other policy goals. We study the generalization performance for such constrained optimization problems, in terms of how well the constraints are satisfied at evaluation time, given that they are satisfied at training time. To improve generalization performance, we frame the problem as a two-player game where one player optimizes the model parameters on a training dataset, and the other player enforces the constraints on an independent validation dataset. We build on recent work in two-player constrained optimization to show that if one uses this two-dataset approach, then constraint generalization can be significantly improved. As we illustrate experimentally, this approach works not only in theory, but also in practice.

Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models. This view will have various implications for NNs, e.g. providing an explanation for why convergence problems arise in NNs, and it gives rough guidance on avoiding overfitting. In addition, we use this phenomenon to predict and confirm a multicollinearity property of NNs not previously reported in the literature. Most importantly, given this loose correspondence, one may choose to routinely use polynomial models instead of NNs, thus avoiding some major problems of the latter, such as having to set many tuning parameters and dealing with convergence issues. We present a number of empirical results; in each case, the accuracy of the polynomial approach matches or exceeds that of NN approaches. A many-featured, open-source software package, polyreg, is available.

Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed simultaneously. To this end, we propose to leverage the spatial structure of a typical oracle by constructing a statistical surrogate for the underlying logistic regression step. We investigate several non-parametric surrogates, including Binomial Gaussian Processes (B-GP), Polynomial, Kernel, and Spline Logistic Regression. In parallel, we develop sampling policies that adaptively balance learning the oracle distribution and learning the root. One of our proposals mimics active learning with B-GPs and provides a novel look-ahead predictive variance formula. The resulting gains of our Spatial PBA algorithm relative to earlier G-PBA models are illustrated with synthetic examples and a challenging stochastic root finding problem from Bermudan option pricing.

Machine learning has the potential to assist many communities in using the large datasets that are becoming more and more available. Unfortunately, much of that potential is not being realized because it would require sharing data in a way that compromises privacy. In order to overcome this hurdle, several methods have been proposed that generate synthetic data while preserving the privacy of the real data. In this paper we consider a key characteristic that synthetic data should have in order to be useful for machine learning researchers - the relative performance of two algorithms (trained and tested) on the synthetic dataset should be the same as their relative performance (when trained and tested) on the original dataset.

Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine learning, in that they are best described as a two-player game between a discriminator and generator. This has yielded both unreliability in the training process, and a general lack of understanding as to how GANs converge, and if so, to what. The purpose of this dissertation is to provide an account of the theory of GANs suitable for the mathematician, highlighting both positive and negative results. This involves identifying the problems when training GANs, and how topological and game-theoretic perspectives of GANs have contributed to our understanding and improved our techniques in recent years.

On the other hand, K-Means has a couple of disadvantages. Firstly, you have to select how many groups/classes there are. This isn't always trivial and ideally with a clustering algorithm we'd want it to figure those out for us because the point of it is to gain some insight from the data. K-means also starts with a random choice of cluster centers and therefore it may yield different clustering results on different runs of the algorithm. Thus, the results may not be repeatable and lack consistency.

We consider the problem of improving fairness when one lacks access to a dataset labeled with protected groups, making it difficult to take advantage of strategies that can improve fairness but require protected group labels, either at training or runtime. To address this, we investigate improving fairness metrics for proxy groups, and test whether doing so results in improved fairness for the true sensitive groups. Results on benchmark and real-world datasets demonstrate that such a proxy fairness strategy can work well in practice. However, we caution that the effectiveness likely depends on the choice of fairness metric, as well as how aligned the proxy groups are with the true protected groups in terms of the constrained model parameters.

We describe the multi-GPU gradient boosting algorithm implemented in the XGBoost library (https://github.com/dmlc/xgboost). Our algorithm allows fast, scalable training on multi-GPU systems with all of the features of the XGBoost library. We employ data compression techniques to minimise the usage of scarce GPU memory while still allowing highly efficient implementation. Using our algorithm we show that it is possible to process 115 million training instances in under three minutes on a publicly available cloud computing instance. The algorithm is implemented using end-to-end GPU parallelism, with prediction, gradient calculation, feature quantisation, decision tree construction and evaluation phases all computed on device.

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of interacting entities. This formulation jointly estimates non-linearities in the underlying data generation, the direct interactions between measured entities, and the indirect effects of unmeasured processes on the observed data. The learning is posed as regularized empirical risk minimization. Details of the algorithm for learning the model are outlined. Experiments demonstrate the performance of the learned model on real data.