Taxonomies are important building blocks of structured knowledge bases, and their construction from text sources and Wikipedia has received much attention. In this paper we focus on the construction of taxonomies for fictional domains, using noisy category systems from fan wikis or text extraction as input. Such fictional domains are archetypes of entity universes that are poorly covered by Wikipedia, such as also enterprise-specific knowledge bases or highly specialized verticals. Our fiction-targeted approach, called TiFi, consists of three phases: (i) category cleaning, by identifying candidate categories that truly represent classes in the domain of interest, (ii) edge cleaning, by selecting subcategory relationships that correspond to class subsumption, and (iii) top-level construction, by mapping classes onto a subset of high-level WordNet categories. A comprehensive evaluation shows that TiFi is able to construct taxonomies for a diverse range of fictional domains such as Lord of the Rings, The Simpsons or Greek Mythology with very high precision and that it outperforms state-of-the-art baselines for taxonomy induction by a substantial margin.

Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the estimators is a challenging non-convex optimization problem. In this paper, we derive new strong convex relaxations for sparse regression. These relaxations are based on the ideal (convex-hull) formulations for rank-one quadratic terms with indicator variables. The new relaxations can be formulated as semidefinite optimization problems in an extended space and are stronger and more general than the state-of-the-art formulations, including the perspective reformulation and formulations with the reverse Huber penalty and the minimax concave penalty functions. Furthermore, the proposed rank-one strengthening can be interpreted as a non-separable, non-convex sparsity-inducing regularizer, which dynamically adjusts its penalty according to the shape of the error function. In our computational experiments with benchmark datasets, the proposed conic formulations are solved within seconds and result in near-optimal solutions (with 0.4\% optimality gap) for non-convex $\ell_0$-problems. Moreover, the resulting estimators also outperform alternative convex approaches from a statistical viewpoint, achieving high prediction accuracy and good interpretability.

Motivation: Human genomic datasets often contain sensitive information that limits use and sharing of the data. In particular, simple anonymisation strategies fail to provide sufficient level of protection for genomic data, because the data are inherently identifiable. Differentially private machine learning can help by guaranteeing that the published results do not leak too much information about any individual data point. Recent research has reached promising results on differentially private drug sensitivity prediction using gene expression data. Differentially private learning with genomic data is challenging because it is more difficult to guarantee the privacy in high dimensions. Dimensionality reduction can help, but if the dimension reduction mapping is learned from the data, then it needs to be differentially private too, which can carry a significant privacy cost. Furthermore, the selection of any hyperparameters (such as the target dimensionality) needs to also avoid leaking private information. Results: We study an approach that uses a large public dataset of similar type to learn a compact representation for differentially private learning. We compare three representation learning methods: variational autoencoders, PCA and random projection. We solve two machine learning tasks on gene expression of cancer cell lines: cancer type classification, and drug sensitivity prediction. The experiments demonstrate significant benefit from all representation learning methods with variational autoencoders providing the most accurate predictions most often. Our results significantly improve over previous state-of-the-art in accuracy of differentially private drug sensitivity prediction.

Motivation: HIV is difficult to treat because its virus mutates at a high rate and mutated viruses easily develop resistance to existing drugs. If the relationships between mutations and drug resistances can be determined from historical data, patients can be provided personalized treatment according to their own mutation information. The HIV Drug Resistance Database was built to investigate the relationships. Our goal is to build a model using data in this database, which simultaneously predicts the resistance of multiple drugs using mutation information from sequences of viruses for any new patient. Results: We propose two variations of a stacking algorithm which borrow information among multiple prediction tasks to improve multivariate prediction performance. The most attractive feature of our proposed methods is the flexibility with which complex multivariate prediction models can be constructed using any univariate prediction models. Using cross-validation studies, we show that our proposed methods outperform other popular multivariate prediction methods. Availability: An R package will be made available.

We tackle the problem of algorithmic fairness, where the goal is to avoid the unfairly influence of sensitive information, in the general context of regression with possible continuous sensitive attributes. We extend the framework of fair empirical risk minimization to this general scenario, covering in this way the whole standard supervised learning setting. Our generalized fairness measure reduces to well known notions of fairness available in literature. We derive learning guarantees for our method, that imply in particular its statistical consistency, both in terms of the risk and the fairness measure. We then specialize our approach to kernel methods and propose a convex fair estimator in that setting. We test the estimator on a commonly used benchmark dataset (Communities and Crime) and on a new dataset collected at the University of Genova, containing the information of the academic career of five thousand students. The latter dataset provides a challenging real case scenario of unfair behaviour of standard regression methods that benefits from our methodology. The experimental results show that our estimator is effective at mitigating the trade-off between accuracy and fairness requirements.

We detail a scheme for scalable, distributed, secure multiparty linear regression at essentially the same speed as plaintext regression. While the core ideas are simple, the recognition of their broad utility when combined is novel. By leveraging a recent advance in secure multiparty principal component analysis, our scheme opens the door to efficient and secure genome-wide association studies across multiple biobanks.

Python's mlrose package provides functionality for implementing some of the most popular randomization and search algorithms, and applying them to a range of different optimization problem domains. In this tutorial, we will discuss how mlrose can be used to find the optimal weights for machine learning models, such as neural networks and regression models. That is, to solve the machine learning weight optimization problem. This is the third in a series of three tutorials about using mlrose to solve randomized optimization problems. Part 1 can be found here and Part 2 can be found here. For a number of different machine learning models, the process of fitting the model parameters involves finding the parameter values that minimize a pre-specified loss function for a given training set.

The distribution of health care payments to insurance plans has substantial consequences for social policy. Risk adjustment formulas predict spending in health insurance markets in order to provide fair benefits and health care coverage for all enrollees, regardless of their health status. Unfortunately, current risk adjustment formulas are known to undercompensate payments to health insurers for specific groups of enrollees (by underpredicting their spending). Much of the existing algorithmic fairness literature for group fairness to date has focused on classifiers and binary outcomes. To improve risk adjustment formulas for undercompensated groups, we expand on concepts from the statistics, computer science, and health economics literature to develop new fair regression methods for continuous outcomes by building fairness considerations directly into the objective function. We additionally propose a novel measure of fairness while asserting that a suite of metrics is necessary in order to evaluate risk adjustment formulas more fully. Our data application using the IBM MarketScan Research Databases and simulation studies demonstrate that these new fair regression methods may lead to massive improvements in group fairness with only small reductions in overall fit.

We present a novel method for learning the weights in multinomial logistic regression based on the alternating direction method of multipliers (ADMM). In each iteration, our algorithm decomposes the training into three steps; a linear least-squares problem for the weights, a global variable update involving a separable cross-entropy loss function, and a trivial dual variable update The least-squares problem can be factorized in the off-line phase, and the separability in the global variable update allows for efficient parallelization, leading to faster convergence. We compare our method with stochastic gradient descent for linear classification as well as for transfer learning and show that the proposed ADMM-Softmax leads to improved generalization and convergence.

We show that model compression can improve the population risk of a pre-trained model, by studying the tradeoff between the decrease in the generalization error and the increase in the empirical risk with model compression. We first prove that model compression reduces an information-theoretic bound on the generalization error; this allows for an interpretation of model compression as a regularization technique to avoid overfitting. We then characterize the increase in empirical risk with model compression using rate distortion theory. These results imply that the population risk could be improved by model compression if the decrease in generalization error exceeds the increase in empirical risk. We show through a linear regression example that such a decrease in population risk due to model compression is indeed possible. Our theoretical results further suggest that the Hessian-weighted $K$-means clustering compression approach can be improved by regularizing the distance between the clustering centers. We provide experiments with neural networks to support our theoretical assertions.