The vast majority of the neural network literature focuses on predicting point values for a given set of response variables, conditioned on a feature vector. In many cases we need to model the full joint conditional distribution over the response variables rather than simply making point predictions. In this paper, we present two novel approaches to such conditional density estimation (CDE): Multiscale Nets (MSNs) and CDE Trend Filtering. Multiscale nets transform the CDE regression task into a hierarchical classification task by decomposing the density into a series of half-spaces and learning boolean probabilities of each split. CDE Trend Filtering applies a k-th order graph trend filtering penalty to the unnormalized logits of a multinomial classifier network, with each edge in the graph corresponding to a neighboring point on a discretized version of the density. We compare both methods against plain multinomial classifier networks and mixture density networks (MDNs) on a simulated dataset and three real-world datasets. The results suggest the two methods are complementary: MSNs work well in a high-data-per-feature regime and CDE-TF is well suited for few-samples-per-feature scenarios where overfitting is a primary concern.

Monte Carlo (MC) sampling algorithms are an extremely widely-used technique to estimate expectations of functions f(x), especially in high dimensions. Control variates are a very powerful technique to reduce the error of such estimates, but in their conventional form rely on having an accurate approximation of f, a priori. Stacked Monte Carlo (StackMC) is a recently introduced technique designed to overcome this limitation by fitting a control variate to the data samples themselves. Done naively, forming a control variate to the data would result in overfitting, typically worsening the MC algorithm's performance. StackMC uses in-sample / out-sample techniques to remove this overfitting. Crucially, it is a post-processing technique, requiring no additional samples, and can be applied to data generated by any MC estimator. Our preliminary experiments demonstrated that StackMC improved the estimates of expectations when it was used to post-process samples produces by a "simple sampling" MC estimator. Here we substantially extend this earlier work. We provide an in-depth analysis of the StackMC algorithm, which we use to construct an improved version of the original algorithm, with lower estimation error. We then perform experiments of StackMC on several additional kinds of MC estimators, demonstrating improved performance when the samples are generated via importance sampling, Latin-hypercube sampling and quasi-Monte Carlo sampling. We also show how to extend StackMC to combine multiple fitting functions, and how to apply it to discrete input spaces x.

We consider the problem of recommending relevant labels (items) for a given data point (user). In particular, we are interested in the practically important setting where the evaluation is with respect to non-decomposable (over labels) performance metrics like the $F_1$ measure, and the training data has missing labels. To this end, we propose a generic framework that given a performance metric $\Psi$, can devise a regularized objective function and a threshold such that all the values in the predicted score vector above and only above the threshold are selected to be positive. We show that the regret or generalization error in the given metric $\Psi$ is bounded ultimately by estimation error of certain underlying parameters. In particular, we derive regret bounds under three popular settings: a) collaborative filtering, b) multilabel classification, and c) PU (positive-unlabeled) learning. For each of the above problems, we can obtain precise non-asymptotic regret bound which is small even when a large fraction of labels is missing. Our empirical results on synthetic and benchmark datasets demonstrate that by explicitly modeling for missing labels and optimizing the desired performance metric, our algorithm indeed achieves significantly better performance (like $F_1$ score) when compared to methods that do not model missing label information carefully.

The analysis of streaming data is one of the biggest challenges posed by the expansion of digital healthcare and bioinformatics. A data stream is a sequence of data that arrives over time. Familiar examples are stock prices, sensor data from mobile devices, personal data from monitoring platforms and many more. The field of machine learning and data mining offers various frameworks for discovering patterns, hidden information, and learning the functional dependencies in complex data. Most methods in machine learning require a good choice of characteristic features to learn functions or compute the posterior probabilities.

We study the problem of structured prediction under test-time budget constraints. We propose a novel approach applicable to a wide range of structured prediction problems in computer vision and natural language processing. Our approach seeks to adaptively generate computationally costly features during test-time in order to reduce the computational cost of prediction while maintaining prediction performance. We show that training the adaptive feature generation system can be reduced to a series of structured learning problems, resulting in efficient training using existing structured learning algorithms. This framework provides theoretical justification for several existing heuristic approaches found in literature. We evaluate our proposed adaptive system on two structured prediction tasks, optical character recognition (OCR) and dependency parsing and show strong performance in reduction of the feature costs without degrading accuracy.

Markov random field (MRF) learning is intractable, and its approximation algorithms are computationally expensive. We target a small subset of MRF that is used frequently in computer vision. We characterize this subset with three concepts: Lattice, Homogeneity, and Inertia; and design a non-markov model as an alternative. Our goal is robust learning from small datasets. Our learning algorithm uses vector quantization and, at time complexity O(U log U) for a dataset of U pixels, is much faster than that of general-purpose MRF.

We propose a novel classification model for weak signal data, building upon a recent model for Bayesian multi-view learning, Group Factor Analysis (GFA). Instead of assuming all data to come from a single GFA model, we allow latent clusters, each having a different GFA model and producing a different class distribution. We show that sharing information across the clusters, by sharing factors, increases the classification accuracy considerably; the shared factors essentially form a flexible noise model that explains away the part of data not related to classification. Motivation for the setting comes from single-trial functional brain imaging data, having a very low signal-to-noise ratio and a natural multi-view setting, with the different sensors, measurement modalities (EEG, MEG, fMRI) and possible auxiliary information as views. We demonstrate our model on a MEG dataset.

Consumers with low demand, like households, are generally supplied single-phase power by connecting their service mains to one of the phases of a distribution transformer. The distribution companies face the problem of keeping a record of consumer connectivity to a phase due to uninformed changes that happen. The exact phase connectivity information is important for the efficient operation and control of distribution system. We propose a new data driven approach to the problem based on Principal Component Analysis (PCA) and its Graph Theoretic interpretations, using energy measurements in equally timed short intervals, generated from smart meters. We propose an algorithm for inferring phase connectivity from noisy measurements. The algorithm is demonstrated using simulated data for phase connectivities in distribution networks.

Autism Spectrum Disorders (ASDs) are often associated with specific atypical postural or motor behaviors, of which Stereotypical Motor Movements (SMMs) have a specific visibility. While the identification and the quantification of SMM patterns remain complex, its automation would provide support to accurate tuning of the intervention in the therapy of autism. Therefore, it is essential to develop automatic SMM detection systems in a real world setting, taking care of strong inter-subject and intra-subject variability. Wireless accelerometer sensing technology can provide a valid infrastructure for real-time SMM detection, however such variability remains a problem also for machine learning methods, in particular whenever handcrafted features extracted from accelerometer signal are considered. Here, we propose to employ the deep learning paradigm in order to learn discriminating features from multi-sensor accelerometer signals. Our results provide preliminary evidence that feature learning and transfer learning embedded in the deep architecture achieve higher accurate SMM detectors in longitudinal scenarios.

We consider the problem of learning the preferences of a heterogeneous population by observing choices from an assortment of products, ads, or other offerings. Our observation model takes a form common in assortment planning applications: each arriving customer is offered an assortment consisting of a subset of all possible offerings; we observe only the assortment and the customer's single choice. In this paper we propose a mixture choice model with a natural underlying low-dimensional structure, and show how to estimate its parameters. In our model, the preferences of each customer or segment follow a separate parametric choice model, but the underlying structure of these parameters over all the models has low dimension. We show that a nuclear-norm regularized maximum likelihood estimator can learn the preferences of all customers using a number of observations much smaller than the number of item-customer combinations. This result shows the potential for structural assumptions to speed up learning and improve revenues in assortment planning and customization. We provide a specialized factored gradient descent algorithm and study the success of the approach empirically.