Measurement-wise Occlusion in Multi-object Tracking

Handling object interaction is a fundamental challenge in practical multi-object tracking, even for simple interactive effects such as one object temporarily occluding another. We formalize the problem of occlusion in tracking with two different abstractions. In object-wise occlusion, objects that are occluded by other objects do not generate measurements. In measurement-wise occlusion, a previously unstudied approach, all objects may generate measurements but some measurements may be occluded by others. While the relative validity of each abstraction depends on the situation and sensor, measurement-wise occlusion fits into probabilistic multi-object tracking algorithms with much looser assumptions on object interaction. Its value is demonstrated by showing that it naturally derives a popular approximation for lidar tracking, and by an example of visual tracking in image space.

Boosting Variational Inference: an Optimization Perspective

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture. However, as is the case with many other variational inference algorithms, its theoretical properties have not been studied. In the present work, we study the convergence properties of this approach from a modern optimization viewpoint by establishing connections to the classic Frank-Wolfe algorithm. Our analyses yields novel theoretical insights regarding the sufficient conditions for convergence, explicit rates, and algorithmic simplifications. Since a lot of focus in previous works for variational inference has been on tractability, our work is especially important as a much needed attempt to bridge the gap between probabilistic models and their corresponding theoretical properties.

Nonparametric Bayesian Sparse Graph Linear Dynamical Systems

A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional sparse random graph to model state transitions. Depending on the sparsity pattern of the corresponding row and column of the graph affinity matrix, a latent state of SGLDS can be categorized as either a non-dynamic state or a dynamic one. A normal-gamma construction is used to shrink the energy captured by the non-dynamic states, while the dynamic states can be further categorized into live, absorbing, or noise-injection states, which capture different types of dynamical components of the underlying time series. The state-of-the-art performance of SGLDS is demonstrated with experiments on both synthetic and real data.

Relaxed Oracles for Semi-Supervised Clustering

Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of allowing "not-sure" answers from a weak oracle and propose an effective algorithm to handle such uncertainties in query responses. Two realistic weak oracle models are considered where ambiguity in answering depends on the distance between two points. We show that a small query complexity is adequate for effective clustering with high probability by providing better pairs to the weak oracle. Experimental results on synthetic and real data show the effectiveness of our approach in overcoming supervision uncertainties and yielding high quality clusters.

Semi-Supervised Active Clustering with Weak Oracles

Semi-supervised active clustering (SSAC) utilizes the knowledge of a domain expert to cluster data points by interactively making pairwise "same-cluster" queries. However, it is impractical to ask human oracles to answer every pairwise query. In this paper, we study the influence of allowing "not-sure" answers from a weak oracle and propose algorithms to efficiently handle uncertainties. Different types of model assumptions are analyzed to cover realistic scenarios of oracle abstraction. In the first model, random-weak oracle, an oracle randomly abstains with a certain probability. We also proposed two distance-weak oracle models which simulate the case of getting confused based on the distance between two points in a pairwise query. For each weak oracle model, we show that a small query complexity is adequate for the effective $k$ means clustering with high probability. Sufficient conditions for the guarantee include a $\gamma$-margin property of the data, and an existence of a point close to each cluster center. Furthermore, we provide a sample complexity with a reduced effect of the cluster's margin and only a logarithmic dependency on the data dimension. Our results allow significantly less number of same-cluster queries if the margin of the clusters is tight, i.e. $\gamma \approx 1$. Experimental results on synthetic data show the effective performance of our approach in overcoming uncertainties.

Optimal Alarms for Vehicular Collision Detection

An important application of intelligent vehicles is advance detection of dangerous events such as collisions. This problem is framed as a problem of optimal alarm choice given predictive models for vehicle location and motion. Techniques for real-time collision detection are surveyed and grouped into three classes: random Monte Carlo sampling, faster deterministic approximations, and machine learning models trained by simulation. Theoretical guarantees on the performance of these collision detection techniques are provided where possible, and empirical analysis is provided for two example scenarios. Results validate Monte Carlo sampling as a robust solution despite its simplicity.

Scalable Greedy Feature Selection via Weak Submodularity

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for each greedy step we need to refit a model or calculate a function using the previously selected choices and the new candidate. Two algorithms that are faster approximations to the greedy forward selection were introduced recently ([Mirzasoleiman et al. 2013, 2015]). They achieve better performance by exploiting distributed computation and stochastic evaluation respectively. Both algorithms have provable performance guarantees for submodular functions. In this paper we show that divergent from previously held opinion, submodularity is not required to obtain approximation guarantees for these two algorithms. Specifically, we show that a generalized concept of weak submodularity suffices to give multiplicative approximation guarantees. Our result extends the applicability of these algorithms to a larger class of functions. Furthermore, we show that a bounded submodularity ratio can be used to provide data dependent bounds that can sometimes be tighter also for submodular functions. We empirically validate our work by showing superior performance of fast greedy approximations versus several established baselines on artificial and real datasets.

Graphical RNN Models

Many time series are generated by a set of entities that interact with one another over time. This paper introduces a broad, flexible framework to learn from multiple inter-dependent time series generated by such entities. Our framework explicitly models the entities and their interactions through time. It achieves this by building on the capabilities of Recurrent Neural Networks, while also offering several ways to incorporate domain knowledge/constraints into the model architecture. The capabilities of our approach are showcased through an application to weather prediction, which shows gains over strong baselines.

Preference Completion from Partial Rankings

We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of observed affinity values. Our approach exploits the observation that while preferences are often recorded as numerical scores, the predictive quantity of interest is the underlying rankings. Thus, attempts to closely match the recorded scores may lead to overfitting and impair generalization performance. Instead, we propose an estimator that directly fits the underlying preference order, combined with nuclear norm constraints to encourage low--rank parameters. Besides (approximate) correctness of the ranking order, the proposed estimator makes no generative assumption on the numerical scores of the observations. One consequence is that the proposed estimator can fit any consistent partial ranking over a subset of the items represented as a directed acyclic graph (DAG), generalizing standard techniques that can only fit preference scores. Despite this generality, for supervision representing total or blockwise total orders, the computational complexity of our algorithm is within a $\log$ factor of the standard algorithms for nuclear norm regularization based estimates for matrix completion. We further show promising empirical results for a novel and challenging application of collaboratively ranking of the associations between brain--regions and cognitive neuroscience terms.

Identifiable Phenotyping using Constrained Non-Negative Matrix Factorization

This work proposes a new algorithm for automated and simultaneous phenotyping of multiple co-occurring medical conditions, also referred as comorbidities, using clinical notes from the electronic health records (EHRs). A basic latent factor estimation technique of non-negative matrix factorization (NMF) is augmented with domain specific constraints to obtain sparse latent factors that are anchored to a fixed set of chronic conditions. The proposed anchoring mechanism ensures a one-to-one identifiable and interpretable mapping between the latent factors and the target comorbidities. Qualitative assessment of the empirical results by clinical experts suggests that the proposed model learns clinically interpretable phenotypes while being predictive of 30 day mortality. The proposed method can be readily adapted to any non-negative EHR data across various healthcare institutions.