Bayesian temporal biclustering with applications to multi-subject neuroscience studies

We consider the problem of analyzing multivariate time series collected on multiple subjects, with the goal of identifying groups of subjects exhibiting similar trends in their recorded measurements over time as well as time-varying groups of associated measurements. To this end, we propose a Bayesian model for temporal biclustering featuring nested partitions, where a time-invariant partition of subjects induces a time-varying partition of measurements. Our approach allows for data-driven determination of the number of subject and measurement clusters as well as estimation of the number and location of changepoints in measurement partitions. To efficiently perform model fitting and posterior estimation with Markov Chain Monte Carlo, we derive a blocked update of measurements' cluster-assignment sequences. We illustrate the performance of our model in two applications to functional magnetic resonance imaging data and to an electroencephalogram dataset. The results indicate that the proposed model can combine information from potentially many subjects to discover a set of interpretable, dynamic patterns. Experiments on simulated data compare the estimation performance of the proposed model against ground-truth values and other statistical methods, showing that it performs well at identifying ground-truth subject and measurement clusters even when no subject or time dependence is present.

Unbiased Learning of Deep Generative Models with Structured Discrete Representations

By composing graphical models with deep learning architectures, we learn generative models with the strengths of both frameworks. The structured variational autoencoder (SVAE) inherits structure and interpretability from graphical models, and flexible likelihoods for high-dimensional data from deep learning, but poses substantial optimization challenges. We propose novel algorithms for learning SVAEs, and are the first to demonstrate the SVAE's ability to handle multimodal uncertainty when data is missing by incorporating discrete latent variables. Our memory-efficient implicit differentiation scheme makes the SVAE tractable to learn via gradient descent, while demonstrating robustness to incomplete optimization. To more rapidly learn accurate graphical model parameters, we derive a method for computing natural gradients without manual derivations, which avoids biases found in prior work. These optimization innovations enable the first comparisons of the SVAE to state-of-the-art time series models, where the SVAE performs competitively while learning interpretable and structured discrete data representations.

Learning Consistent Deep Generative Models from Sparse Data via Prediction Constraints

We develop a new framework for learning variational autoencoders and other deep generative models that balances generative and discriminative goals. Our framework optimizes model parameters to maximize a variational lower bound on the likelihood of observed data, subject to a task-specific prediction constraint that prevents model misspecification from leading to inaccurate predictions. We further enforce a consistency constraint, derived naturally from the generative model, that requires predictions on reconstructed data to match those on the original data. We show that these two contributions -- prediction constraints and consistency constraints -- lead to promising image classification performance, especially in the semi-supervised scenario where category labels are sparse but unlabeled data is plentiful. Our approach enables advances in generative modeling to directly boost semi-supervised classification performance, an ability we demonstrate by augmenting deep generative models with latent variables capturing spatial transformations.

Clouds of Oriented Gradients for 3D Detection of Objects, Surfaces, and Indoor Scene Layouts

We develop new representations and algorithms for three-dimensional (3D) object detection and spatial layout prediction in cluttered indoor scenes. We first propose a clouds of oriented gradient (COG) descriptor that links the 2D appearance and 3D pose of object categories, and thus accurately models how perspective projection affects perceived image gradients. To better represent the 3D visual styles of large objects and provide contextual cues to improve the detection of small objects, we introduce latent support surfaces. We then propose a "Manhattan voxel" representation which better captures the 3D room layout geometry of common indoor environments. Effective classification rules are learned via a latent structured prediction framework. Contextual relationships among categories and layout are captured via a cascade of classifiers, leading to holistic scene hypotheses that exceed the state-of-the-art on the SUN RGB-D database.

Multi-layer Depth and Epipolar Feature Transformers for 3D Scene Reconstruction

We tackle the problem of automatically reconstructing a complete 3D model of a scene from a single RGB image. This challenging task requires inferring the shape of both visible and occluded surfaces. Our approach utilizes viewer-centered, multi-layer representation of scene geometry adapted from recent methods for single object shape completion. To improve the accuracy of view-centered representations for complex scenes, we introduce a novel "Epipolar Feature Transformer" that transfers convolutional network features from an input view to other virtual camera viewpoints, and thus better covers the 3D scene geometry. Unlike existing approaches that first detect and localize objects in 3D, and then infer object shape using category-specific models, our approach is fully convolutional, end-to-end differentiable, and avoids the resolution and memory limitations of voxel representations. We demonstrate the advantages of multi-layer depth representations and epipolar feature transformers on the reconstruction of a large database of indoor scenes.

A Fusion Approach for Multi-Frame Optical Flow Estimation

To date, top-performing optical flow estimation methods only take pairs of consecutive frames into account. While elegant and appealing, the idea of using more than two frames has not yet produced state-of-the-art results. We present a simple, yet effective fusion approach for multi-frame optical flow that benefits from longer-term temporal cues. Our method first warps the optical flow from previous frames to the current, thereby yielding multiple plausible estimates. It then fuses the complementary information carried by these estimates into a new optical flow field. At the time of submission, our method ranks first among published flow methods in the MPI Sintel and KITTI 2015 benchmarks.

Bayesian Paragraph Vectors

Word2vec (Mikolov et al., 2013) has proven to be successful in natural language processing by capturing the semantic relationships between different words. Built on top of single-word embeddings, paragraph vectors (Le and Mikolov, 2014) find fixed-length representations for pieces of text with arbitrary lengths, such as documents, paragraphs, and sentences. In this work, we propose a novel interpretation for neural-network-based paragraph vectors by developing an unsupervised generative model whose maximum likelihood solution corresponds to traditional paragraph vectors. This probabilistic formulation allows us to go beyond point estimates of parameters and to perform Bayesian posterior inference. We find that the entropy of paragraph vectors decreases with the length of documents, and that information about posterior uncertainty improves performance in supervised learning tasks such as sentiment analysis and paraphrase detection.

Prediction-Constrained Topic Models for Antidepressant Recommendation

Supervisory signals can help topic models discover low-dimensional data representations that are more interpretable for clinical tasks. We propose a framework for training supervised latent Dirichlet allocation that balances two goals: faithful generative explanations of high-dimensional data and accurate prediction of associated class labels. Existing approaches fail to balance these goals by not properly handling a fundamental asymmetry: the intended task is always predicting labels from data, not data from labels. Our new prediction-constrained objective trains models that predict labels from heldout data well while also producing good generative likelihoods and interpretable topic-word parameters. In a case study on predicting depression medications from electronic health records, we demonstrate improved recommendations compared to previous supervised topic models and high- dimensional logistic regression from words alone.

Cascaded Scene Flow Prediction using Semantic Segmentation

Given two consecutive frames from a pair of stereo cameras, 3D scene flow methods simultaneously estimate the 3D geometry and motion of the observed scene. Many existing approaches use superpixels for regularization, but may predict inconsistent shapes and motions inside rigidly moving objects. We instead assume that scenes consist of foreground objects rigidly moving in front of a static background, and use semantic cues to produce pixel-accurate scene flow estimates. Our cascaded classification framework accurately models 3D scenes by iteratively refining semantic segmentation masks, stereo correspondences, 3D rigid motion estimates, and optical flow fields. We evaluate our method on the challenging KITTI autonomous driving benchmark, and show that accounting for the motion of segmented vehicles leads to state-of-the-art performance.

Prediction-Constrained Training for Semi-Supervised Mixture and Topic Models

Supervisory signals have the potential to make low-dimensional data representations, like those learned by mixture and topic models, more interpretable and useful. We propose a framework for training latent variable models that explicitly balances two goals: recovery of faithful generative explanations of high-dimensional data, and accurate prediction of associated semantic labels. Existing approaches fail to achieve these goals due to an incomplete treatment of a fundamental asymmetry: the intended application is always predicting labels from data, not data from labels. Our prediction-constrained objective for training generative models coherently integrates loss-based supervisory signals while enabling effective semi-supervised learning from partially labeled data. We derive learning algorithms for semi-supervised mixture and topic models using stochastic gradient descent with automatic differentiation. We demonstrate improved prediction quality compared to several previous supervised topic models, achieving predictions competitive with high-dimensional logistic regression on text sentiment analysis and electronic health records tasks while simultaneously learning interpretable topics.