State space models (SSMs) are a flexible approach to modeling complex time series. However, inference in SSMs is often computationally prohibitive for long time series. Stochastic gradient MCMC (SGMCMC) is a popular method for scalable Bayesian inference for large independent data. Unfortunately when applied to dependent data, such as in SSMs, SGMCMC's stochastic gradient estimates are biased as they break crucial temporal dependencies. To alleviate this, we propose stochastic gradient estimators that control this bias by performing additional computation in a `buffer' to reduce breaking dependencies. Furthermore, we derive error bounds for this bias and show a geometric decay under mild conditions. Using these estimators, we develop novel SGMCMC samplers for discrete, continuous and mixed-type SSMs. Our experiments on real and synthetic data demonstrate the effectiveness of our SGMCMC algorithms compared to batch MCMC, allowing us to scale inference to long time series with millions of time points.

Deep neural networks (DNNs) are computationally/memory-intensive and vulnerable to adversarial attacks, making them prohibitive in some real-world applications. By converting dense models into sparse ones, pruning appears to be a promising solution to reducing the computation/memory cost. This paper studies classification models, especially DNN-based ones, to demonstrate that there exists intrinsic relationships between their sparsity and adversarial robustness. Our analyses reveal, both theoretically and empirically, that nonlinear DNN-based classifiers behave differently under $l_2$ attacks from some linear ones. We further demonstrate that an appropriately higher model sparsity implies better robustness of nonlinear DNNs, whereas over-sparsified models can be more difficult to resist adversarial examples.

Abstract--In the era of "big data", analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are employed, a crucial step is to select the most appropriate model or method from a set of candidates. Model selection is a key ingredient in data analysis for reliable and reproducible statistical inference or prediction, and thus central to scientific studies in fields such as ecology, economics, engineering, finance, political science, biology, and epidemiology. There has been a long history of model selection techniques that arise from researches in statistics, information theory, and signal processing. A considerable number of methods have been proposed, following different philosophies and exhibiting varying performances. The purpose of this article is to bring a comprehensive overview of them, in terms of their motivation, large sample performance, and applicability. We provide integrated and practically relevant discussions on theoretical properties of state-ofthe-art model selection approaches. We also share our thoughts on some controversial views on the practice of model selection. Vast development in hardware storage, precision instrument manufacture, economic globalization, etc. have generated huge volumes of data that can be analyzed to extract useful information. Typical statistical inference or machine learning procedures learn from and make predictions on data by fitting parametric or nonparametric models (in a broad sense). However, there exists no model that is universally suitable for any data and goal. This research was funded in part by the Defense Advanced Research Projects Agency (DARPA) under grant number W911NF-18-1-0134. J. Ding and Y. Yang are with the School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, United States. V. Tarokh is with the Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, United States. Therefore, a crucial step in a typical data analysis is to consider a set of candidate models (referred to as the model class), and then select the most appropriate one. In other words, model selection is the task of selecting a statistical model from a model class, given a set of data. There have been many overview papers on model selection scattered in the communities of signal processing [1], statistics [2], machine learning [3], epidemiology [4], chemometrics [5], ecology and evolution [6]. Despite the abundant literature on model selection, existing overviews usually focus on derivations, descriptions, or applications of particular model selection principles.

Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However, without proper tuning, this technique implies a high rejection rate. Several methods have been explored to cope with this problem, based on the principle of adaptively estimating the density by a simpler function, using the information of the previous samples. Most of them either rely on strong assumptions on the form of the density, or do not offer any theoretical performance guarantee. We give the first theoretical lower bound for the problem of adaptive rejection sampling and introduce a new algorithm which guarantees a near-optimal rejection rate in a minimax sense.

We study convergence properties of Stochastic Gradient Descent (SGD) for convex objectives without assumptions on smoothness or strict convexity. We consider the question of establishing that with high probability the objective evaluated at the candidate minimizer returned by SGD is close to the minimal value of the objective. We compare this result concerning the final candidate minimzer (i.e. the final model parameters learned after all gradient steps) to the online learning techniques of [Zin03] that take a rolling average of the model parameters at the different steps of SGD.

Generalized additive models (GAMs) are favored in many regression and binary classification problems because they are able to fit complex, nonlinear functions while still remaining interpretable. In the first part of this paper, we generalize a state-of-the-art GAM learning algorithm based on boosted trees to the multiclass setting, and show that this multiclass algorithm outperforms existing GAM fitting algorithms and sometimes matches the performance of full complex models. In the second part, we turn our attention to the interpretability of GAMs in the multiclass setting. Surprisingly, the natural interpretability of GAMs breaks down when there are more than two classes. Drawing inspiration from binary GAMs, we identify two axioms that any additive model must satisfy to not be visually misleading. We then develop a post-processing technique (API) that provably transforms pretrained additive models to satisfy the interpretability axioms without sacrificing accuracy. The technique works not just on models trained with our algorithm, but on any multiclass additive model. We demonstrate API on a 12-class infant-mortality dataset.

This analysis explores the temporal sequencing of objects in a movie trailer. Temporal sequencing of objects in a movie trailer (e.g., a long shot of an object vs intermittent short shots) can convey information about the type of movie, plot of the movie, role of the main characters, and the filmmakers cinematographic choices. When combined with historical customer data, sequencing analysis can be used to improve predictions of customer behavior. E.g., a customer buys tickets to a new movie and maybe the customer has seen movies in the past that contained similar sequences. To explore object sequencing in movie trailers, we propose a video convolutional network to capture actions and scenes that are predictive of customers' preferences. The model learns the specific nature of sequences for different types of objects (e.g., cars vs faces), and the role of sequences in predicting customer future behavior. We show how such a temporal-aware model outperforms simple feature pooling methods proposed in our previous works and, importantly, demonstrate the additional model explain-ability allowed by such a model.

Tuning machine learning models, particularly deep learning architectures, is a complex process. Automated hyperparameter tuning algorithms often depend on specific optimization metrics. However, in many situations, a developer trades one metric against another: accuracy versus overfitting, precision versus recall, smaller models and accuracy, etc. With deep learning, not only are the model's representations opaque, the model's behavior when parameters "knobs" are changed may also be unpredictable. Thus, picking the "best" model often requires time-consuming model comparison. In this work, we introduce LAMVI-2, a visual analytics system to support a developer in comparing hyperparameter settings and outcomes. By focusing on word-embedding models ("deep learning for text") we integrate views to compare both high-level statistics as well as internal model behaviors (e.g., comparing word 'distances'). We demonstrate how developers can work with LAMVI-2 to more quickly and accurately narrow down an appropriate and effective application-specific model.

One of the common tasks in unsupervised learning is dimensionality reduction, where the goal is to find meaningful low-dimensional structures hidden in high-dimensional data. Sometimes referred to as manifold learning, this problem is closely related to the problem of localization, which aims at embedding a weighted graph into a low-dimensional Euclidean space. Several methods have been proposed for localization, and also manifold learning. Nonetheless, the robustness property of most of them is little understood. In this paper, we obtain perturbation bounds for classical scaling and trilateration, which are then applied to derive performance bounds for Isomap, Landmark Isomap, and Maximum Variance Unfolding. A new perturbation bound for procrustes analysis plays a key role.

Models for predicting aircraft motion are an important component of modern aeronautical systems. These models help aircraft plan collision avoidance maneuvers and help conduct offline performance and safety analyses. In this article, we develop a method for learning a probabilistic generative model of aircraft motion in terminal airspace, the controlled airspace surrounding a given airport. The method fits the model based on a historical dataset of radar-based position measurements of aircraft landings and takeoffs at that airport. We find that the model generates realistic trajectories, provides accurate predictions, and captures the statistical properties of aircraft trajectories. Furthermore, the model trains quickly, is compact, and allows for efficient real-time inference.