Predicting the future behavior of road users is one of the most challenging and important problems in autonomous driving. Applying deep learning to this problem requires fusing heterogeneous world state in the form of rich perception signals and map information, and inferring highly multi-modal distributions over possible futures. In this paper, we present MultiPath++, a future prediction model that achieves state-of-the-art performance on popular benchmarks. MultiPath++ improves the MultiPath architecture [34] by revisiting many design choices. The first key design difference is a departure from dense image-based encoding of the input world state in favor of a sparse encoding of heterogeneous scene elements: MultiPath++ consumes compact and efficient polylines to describe road features, and raw agent state information directly (e.g., position, velocity, acceleration). We propose a context-aware fusion of these elements and develop a reusable multi-context gating fusion component. Second, we reconsider the choice of pre-defined static anchors, and develop a way to learn latent anchor embeddings end-to-end in the model. Lastly, we explore ensembling and output aggregation techniques—common in other ML domains—and find effective variants for our probabilistic multimodal output representation. We perform an extensive ablation on these design choices, and show that our proposed model achieves state-of-the-art performance on the Argoverse Motion Forecasting Competition [10] and the Waymo Open Dataset Motion Prediction Challenge [13].

We propose a framework for modeling and estimating the state of controlled dynamical systems, where an agent can affect the system through actions and receives partial observations. Based on this framework, we propose Predictive State Representation with Random Fourier Features (RFF-PSR). A key property in RFF-PSRs is that the state estimate is represented by a conditional distribution of future observations given future actions. RFFPSRs combine this representation with moment-matching, kernel embedding, and local optimization to achieve a method that enjoys several favorable qualities: It can represent controlled environments which can be affected by actions, it has an efficient and theoretically justified learning algorithm, it uses a non-parametric representation that has expressive power to represent continuous non-linear dynamics. We provide a detailed formulation, a theoretical analysis and an experimental evaluation that demonstrates the effectiveness of our method.

We introduce Recurrent Predictive State Policy(RPSP) networks, a recurrent architecture that brings insights from predictive state representations to reinforcement learning in partially ob-servable environments. Predictive state policy networks consist of a recursive filter, which keeps track of a belief about the state of the environment, and a reactive policy that directly maps beliefs to actions, to maximize the cumulative reward. The recursive filter leverages predictive state representations (PSRs) (Rosencrantz & Gordon, 2004; Sun et al., 2016) by modeling predictive state{—}a prediction of the distribution of future observations conditioned on history and future actions.This representation gives rise to a rich class of statistically consistent algorithms (Hefny et al.,2017) to initialize the recursive filter. Predictive stats serves as an equivalent representation of a belief state. Therefore, the policy component of the RPSP-network can be purely reactive, simplifying training while still allowing optimal behavior. Moreover, we use the PSR interpretation during training as well, by incorporating prediction error in the loss function. The entire network (recursive filter and reactive policy) is still differentiable and can be trained using gradient-based methods. We optimize our policy using a combination of policy gradient based on rewards (Williams, 1992)and gradient descent based on prediction error.We show the efficacy of RPSP-networks on a set of robotic control tasks from OpenAI Gym. We empirically show that RPSP-networks perform well compared with memory-preserving networks such as GRUs, as well as finite memory models, being the overall best performing method.

The first step towards an autonomous database management system (DBMS) is the ability to model the target application's workload. This is necessary to allow the system to anticipate future workload needs and select the proper optimizations in a timely manner. Previous forecasting techniques model the resource utilization of the queries. Such metrics, however, change whenever the physical design of the database and the hardware resources change, thereby rendering previous forecasting models useless.

We present a new model, Predictive State Recurrent Neural Networks (PSRNNs), for filtering and prediction in dynamical systems. PSRNNs draw on insights from both Recurrent Neural Networks (RNNs) and Predictive State Representations (PSRs), and inherit advantages from both types of models. Like many successful RNN architectures, PSRNNs use (potentially deeply composed) bilinear transfer functions to combine information from multiple sources. We show that such bilinear functions arise naturally from state updates in Bayes filters like PSRs, in which observations can be viewed as gating belief states. We also show that PSRNNs can be learned effectively by combining Backpropogation Through Time (BPTT) with an initialization derived from a statistically consistent learning algorithm for PSRs called two-stage regression (2SR). Finally, we show that PSRNNs can be factorized using tensor decomposition, reducing model size and suggesting interesting connections to existing multiplicative architectures such as LSTMs and GRUs. We apply PSRNNs to 4 datasets, and show that we outperform several popular alternative approaches to modeling dynamical systems in all cases.

We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient descent (SGD); but their theoretical analysis almost exclusively assumes convexity. In contrast, we prove non-asymptotic rates of convergence (to stationary points) of SVRG for nonconvex optimization, and show that it is provably faster than SGD and gradient descent. We also analyze a subclass of nonconvex problems on which SVRG attains linear convergence to the global optimum. We extend our analysis to mini-batch variants of SVRG, showing (theoretical) linear speedup due to minibatching in parallel settings.

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoffbetween computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporateprior information such as sparsity or structure. To address this problem, we presenta new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, therebyallowing users to incorporate prior knowledge via standard techniques such asL 1 regularization. Many existing spectral methods are special cases of this newframework, using linear regression as the supervised learner. We demonstrate theeffectiveness of our framework by showing examples where nonlinear regressionor lasso let us learn better state representations than plain linear regression does;the correctness of these instances follows directly from our general analysis.

We study optimization algorithms based on variance reduction for stochastic gradientdescent (SGD). Remarkable recent progress has been made in this directionthrough development of algorithms like SAG, SVRG, SAGA. These algorithmshave been shown to outperform SGD, both theoretically and empirically. However,asynchronous versions of these algorithms—a crucial requirement for modernlarge-scale applications—have not been studied. We bridge this gap by presentinga unifying framework that captures many variance reduction techniques.Subsequently, we propose an asynchronous algorithm grounded in our framework,with fast convergence rates. An important consequence of our general approachis that it yields asynchronous versions of variance reduction algorithms such asSVRG, SAGA as a byproduct. Our method achieves near linear speedup in sparsesettings common to machine learning. We demonstrate the empirical performanceof our method through a concrete realization of asynchronous SVRG.

What does a user do when he logs in to the Twitter website? Does he merely browse through the tweets of all his friends as a source of information for his own tweets, or does he simply tweet a message of his own personal interest? Does he skim through the tweets of all his friends or only of a selected few? A number of factors might influence a user in these decisions. Does this social influence vary across cultures? In our work, we propose a simple yet effective model to predict the behavior of a user - in terms of which hashtag or named entity he might include in his future tweets. We have approached the problem as a classification task with the various influences contributing as features. Further, we analyze the contribution of the weights of the different features. Using our model we analyze data from different cultures and discover interesting differences in social influence.

A single, stationary topic model such as latent Dirichlet allocation is inappropriate for modeling corpora that span long time periods, as the popularity of topics is likely to change over time. A number of models that incorporate time have been proposed, but in general they either exhibit limited forms of temporal variation, or require computationally expensive inference methods. In this paper we propose nonparametric Topics over Time (npTOT), a model for time-varying topics that allows an unbounded number of topics and flexible distribution over the temporal variations in those topics’ popularity. We develop a collapsed Gibbs sampler for the proposed model and compare against existing models on synthetic and real document sets.