We present a semi-supervised learning algorithm for learning discrete factor analysis models with arbitrary structure on the latent variables. Our algorithm assumes that every latent variable has an "anchor", an observed variable with only that latent variable as its parent. Given such anchors, we show that it is possible to consistently recover moments of the latent variables and use these moments to learn complete models. We also introduce a new technique for improving the robustness of method-of-moment algorithms by optimizing over the marginal polytope or its relaxations. We evaluate our algorithm using two real-world tasks, tag prediction on questions from the Stack Overflow website and medical diagnosis in an emergency department.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.It is available as a free download under a Creative Commons license. You are free to share the book, translate it, or remix it. Before you is a tool for learning basic data mining techniques. Most data mining textbooks focus on providing a theoretical foundation for data mining, and as result, may seem notoriously difficult to understand. Don't get me wrong, the information in those books is extremely important.

One approach for constructing copula functions is by multiplication. Given that products of cumulative distribution functions (CDFs) are also CDFs, an adjustment to this multiplication will result in a copula model, as discussed by Liebscher (J Mult Analysis, 2008). Parameterizing models via products of CDFs has some advantages, both from the copula perspective (e.g., it is well-defined for any dimensionality) and from general multivariate analysis (e.g., it provides models where small dimensional marginal distributions can be easily read-off from the parameters). Independently, Huang and Frey (J Mach Learn Res, 2011) showed the connection between certain sparse graphical models and products of CDFs, as well as message-passing (dynamic programming) schemes for computing the likelihood function of such models. Such schemes allows models to be estimated with likelihood-based methods. We discuss and demonstrate MCMC approaches for estimating such models in a Bayesian context, their application in copula modeling, and how message-passing can be strongly simplified. Importantly, our view of message-passing opens up possibilities to scaling up such methods, given that even dynamic programming is not a scalable solution for calculating likelihood functions in many models.

A Kronecker product model is the set of visible marginal probability distributions of an exponential family whose sufficient statistics matrix factorizes as a Kronecker product of two matrices, one for the visible variables and one for the hidden variables. We estimate the dimension of these models by the maximum rank of the Jacobian in the limit of large parameters. The limit is described by the tropical morphism; a piecewise linear map with pieces corresponding to slicings of the visible matrix by the normal fan of the hidden matrix. We obtain combinatorial conditions under which the model has the expected dimension, equal to the minimum of the number of natural parameters and the dimension of the ambient probability simplex. Additionally, we prove that the binary restricted Boltzmann machine always has the expected dimension.

This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive scoring functions, and we derive non-asymptotic risk bounds under a sparsity assumption. In particular, oracle inequalities in probability holding under a margin condition assess the performance of our procedure, and prove its minimax optimality. An MCMC-flavored algorithm is proposed to implement our method, along with its behavior on synthetic and real-life datasets.

Computing the marginal likelihood (ML) of a model requires marginalizing out all of the parameters and latent variables, a difficult high-dimensional summation or integration problem. To make matters worse, it is often hard to measure the accuracy of one's ML estimates. We present bidirectional Monte Carlo, a technique for obtaining accurate log-ML estimates on data simulated from a model. This method obtains stochastic lower bounds on the log-ML using annealed importance sampling or sequential Monte Carlo, and obtains stochastic upper bounds by running these same algorithms in reverse starting from an exact posterior sample. The true value can be sandwiched between these two stochastic bounds with high probability. Using the ground truth log-ML estimates obtained from our method, we quantitatively evaluate a wide variety of existing ML estimators on several latent variable models: clustering, a low rank approximation, and a binary attributes model. These experiments yield insights into how to accurately estimate marginal likelihoods.

Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair treatment do not result from decision making or predictions made via machine learning. In this work, we introduce a novel empirical risk minimization (ERM) framework for supervised learning, neutralized ERM (NERM) that ensures that any classifiers obtained can be guaranteed to be neutral with respect to a viewpoint hypothesis. More specifically, given a viewpoint hypothesis, NERM works to find a target hypothesis that minimizes the empirical risk while simultaneously identifying a target hypothesis that is neutral to the viewpoint hypothesis. Within the NERM framework, we derive a theoretical bound on empirical and generalization neutrality risks. Furthermore, as a realization of NERM with linear classification, we derive a max-margin algorithm, neutral support vector machine (SVM). Experimental results show that our neutral SVM shows improved classification performance in real datasets without sacrificing the neutrality guarantee.

We aim to produce predictive models that are not only accurate, but are also interpretable to human experts. Our models are decision lists, which consist of a series of if...then... statements (e.g., if high blood pressure, then stroke) that discretize a high-dimensional, multivariate feature space into a series of simple, readily interpretable decision statements. We introduce a generative model called Bayesian Rule Lists that yields a posterior distribution over possible decision lists. It employs a novel prior structure to encourage sparsity. Our experiments show that Bayesian Rule Lists has predictive accuracy on par with the current top algorithms for prediction in machine learning. Our method is motivated by recent developments in personalized medicine, and can be used to produce highly accurate and interpretable medical scoring systems. We demonstrate this by producing an alternative to the CHADS$_2$ score, actively used in clinical practice for estimating the risk of stroke in patients that have atrial fibrillation. Our model is as interpretable as CHADS$_2$, but more accurate.

We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in (0, \, \infty)$, and allow for arbitrary covariance among the features. For both methods, we provide an explicit and efficiently computable expression for the limiting predictive risk, which depends only on the spectrum of the feature-covariance matrix, the signal strength, and the aspect ratio $\gamma$. Especially in the case of regularized discriminant analysis, we find that predictive accuracy has a nuanced dependence on the eigenvalue distribution of the covariance matrix, suggesting that analyses based on the operator norm of the covariance matrix may not be sharp. Our results also uncover several qualitative insights about both methods: for example, with ridge regression, there is an exact inverse relation between the limiting predictive risk and the limiting estimation risk given a fixed signal strength. Our analysis builds on recent advances in random matrix theory.

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporate prior information such as sparsity or structure. To address this problem, we present a new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as L1 regularization. Many existing spectral methods are special cases of this new framework, using linear regression as the supervised learner. We demonstrate the effectiveness of our framework by showing examples where nonlinear regression or lasso let us learn better state representations than plain linear regression does; the correctness of these instances follows directly from our general analysis.