UAI 2019 Papers

Transportation service providers that dispatch drivers and vehicles to riders start to support both on-demand ride requests posted in real time and rides scheduled in advance, leading to new challenges which, to the best of our knowledge, have not been addressed by existing works. To fill the gap, we design novel trip-vehicle dispatch algorithms to handle both types of requests while taking into account an estimated request distribution of on-demand requests. At the core of the algorithms is the newly proposed Constrained Spatio-Temporal value function (CST-function), which is polynomial-time computable and represents the expected value a vehicle could gain with the constraint that it needs to arrive at a specific location at a given time. Built upon CST-function, we design a randomized best-fit algorithm for scheduled requests and an online planning algorithm for on-demand requests given the scheduled requests as constraints. We evaluate the algorithms through extensive experiments on a real-world dataset of an online ride-hailing platform.

Domain generalization (DG) aims to incorporate knowledge from multiple source domains into a single model that could generalize well on unseen target domains. This problem is ubiquitous in practice since the distributions of the target data may rarely be identical to those of the source data. In this paper, we propose Multidomain Discriminant Analysis (MDA) to address DG of classification tasks in general situations. MDA learns a domain-invariant feature transformation that aims to achieve appealing properties, including a minimal divergence among domains within each class, a maximal separability among classes, and overall maximal compactness of all classes. Furthermore, we provide the bounds on excess risk and generalization error by learning theory analysis. Comprehensive experiments on synthetic and real benchmark datasets demonstrate the effectiveness of MDA.

Scientific imaging techniques such as optical and electron microscopy and computed tomography (CT) scanning are used to study the 3D structure of an object through 2D observations. These observations are related to the original 3D object through orthogonal integral projections. For common 3D reconstruction algorithms, computational efficiency requires the modeling of the 3D structures to take place in Fourier space by applying the Fourier slice theorem. At present, it is unclear how to differentiate through the projection operator, and hence current learning algorithms can not rely on gradient based methods to optimize 3D structure models. In this paper we show how back-propagation through the projection operator in Fourier space can be achieved. We demonstrate the validity of the approach with experiments on 3D reconstruction of proteins. We further extend our approach to learning probabilistic models of 3D objects. This allows us to predict regions of low sampling rates or estimate noise. A higher sample efficiency can be reached by utilizing the learned uncertainties of the 3D structure as an unsupervised estimate of the model fit. Finally, we demonstrate how the reconstruction algorithm can be extended with an amortized inference scheme on unknown attributes such as object pose. Through empirical studies we show that joint inference of the 3D structure and the object pose becomes more difficult when the ground truth object contains more symmetries. Due to the presence of for instance (approximate) rotational symmetries, the pose estimation can easily get stuck in local optima, inhibiting a fine-grained high-quality estimate of the 3D structure.

Larger networks generally have greater representational power at the cost of increased computational complexity. Sparsifying such networks has been an active area of research but has been generally limited to static regularization or dynamic approaches using reinforcement learning. We explore a mixture of experts (MoE) approach to deep dynamic routing, which activates certain experts in the network on a per-example basis. Our novel DeepMoE architecture increases the representational power of standard convolutional networks by adaptively sparsifying and recalibrating channel-wise features in each convolutional layer. We employ a multi-headed sparse gating network to determine the selection and scaling of channels for each input, leveraging exponential combinations of experts within a single convolutional network. Our proposed architecture is evaluated on four benchmark datasets and tasks, and we show that Deep-MoEs are able to achieve higher accuracy with lower computation than standard convolutional networks.

Momentum is a popular technique to accelerate the convergence in practical training, and its impact on convergence guarantee has been well-studied for first-order algorithms. However, such a successful acceleration technique has not yet been proposed for second-order algorithms in nonconvex optimization. In this paper, we apply the momentum scheme to cubic regularized (CR) Newton’s method and explore the potential for acceleration. Our numerical experiments on various nonconvex optimization problems demonstrate that the momentum scheme can substantially facilitate the convergence of cubic regularization, and perform even better than the Nesterov’s acceleration scheme for CR. Theoretically, we prove that CR under momentum achieves the best possible convergence rate to a second-order stationary point for nonconvex optimization. Moreover, we study the proposed algorithm for solving problems satisfying an error bound condition and establish a local quadratic convergence rate. Then, particularly for finite-sum problems, we show that the proposed algorithm can allow computational inexactness that reduces the overall sample complexity without degrading the convergence rate.

Probabilistic survival predictions (i.e. personalized survival curves) from models trained with Maximum Likelihood Estimation (MLE) can have high, and sometimes unacceptably high variance. The field of meteorology, where the paradigm of maximizing sharpness subject to calibration is popular, has addressed this problem by using scoring rules beyond MLE, such as the Continuous Ranked Probability Score (CRPS). In this paper we present the \emph{Survival-CRPS}, a generalization of the CRPS to the survival prediction setting, with right-censored and interval-censored variants. We evaluate our ideas on the mortality prediction task using two different Electronic Health Record (EHR) data sets (STARR and MIMIC-III) covering millions of patients, with suitable deep neural network architectures: a Recurrent Neural Network (RNN) for STARR and a Fully Connected Network (FCN) for MIMIC-III. We compare results between the two different scoring rules while keeping the network architecture and data fixed, and show that models trained with Survival-CRPS result in sharper predictive distributions compared to those trained by MLE, while still maintaining calibration.

Aggregation systems (e.g., Uber, Lyft, Food- Panda, Deliveroo) have been increasingly used to improve efficiency in numerous environments, including in transportation, logistics, food and grocery delivery. In these systems, a centralized entity (e.g., Uber) aggregates sup- ply and assigns them to demand so as to optimize a central metric such as profit, number of requests, delay etc. Due to optimizing a metric of importance to the centralized entity, the interests of individuals (e.g., drivers, de- livery boys) can be sacrificed. Therefore, in this paper, we focus on the problem of serving individual interests, i.e., learning revenue maximizing policies for individuals in the presence of a self interested central entity. Since there are large number of learning agents that are homogenous, we represent the problem as an Anonymous Multi-Agent Reinforcement Learn- ing (AyMARL) problem. By using the self interested centralized entity as a correlation entity, we provide a novel learning mechanism that helps individual agents to maximize their individual revenue. Our Correlated Learning (CL) algorithm is able to outperform existing mechanisms on a generic simulator for aggregation systems and multiple other benchmark Multi-Agent Reinforcement Learning (MARL) problems.

We study data-driven assistants that provide congestion forecasts to users of shared facilities (roads, cafeterias, etc.), to support coordination between them, and increase efficiency of such collective systems. Key questions are: (1) when and how much can (accurate) predictions help for coordination, and (2) which assistant algorithms reach optimal predictions? First we lay conceptual ground for this setting where user preferences are a priori unknown and predictions influence outcomes. Addressing (1), we establish conditions under which self-fulfilling prophecies, i.e., “perfect” (probabilistic) predictions of what will happen, solve the coordination problem in the gametheoretic sense of selecting a Bayesian Nash equilibrium (BNE). Next we prove that such prophecies exist even in large-scale settings where only aggregated statistics about users are available. This entails a new (nonatomic) BNE existence result. Addressing (2), we propose two assistant algorithms that sequentially learn from users’ reactions, together with optimality/ convergence guarantees. We validate one of them in a large real-world experiment.

Considering a class of gradient-based multi-agent learning algorithms in non-cooperative settings, we provide convergence guarantees to a neighborhood of a stable Nash equilibrium. In particular, we consider continuous games where agents learn in 1) deterministic settings with oracle access to their gradient and 2) stochastic settings with an unbiased estimator of their gradient. We also study the effects of non-uniform learning rates, which causes a distortion of the vector field that can alter which equilibrium the agents converge to and the path they take. We support the analysis with numerical examples that provide insight into how one might synthesize games to achieve desired equilibria.

Expectation propagation (EP) is a powerful approximate inference algorithm. However, a critical barrier in applying EP is that the moment matching in message updates can be intractable. Handcrafting approximations is usually tricky, and lacks generalizability. Importance sampling is very expensive. While Laplace propagation offers an excellent solution, it has to run numerical optimizations to find Laplace approximations in every update, which is still quite inefficient. To overcome these practical barriers, we propose conditional expectation propagation (CEP) that performs conditional moment matching given the variables outside each message fixed, and then takes expectation w.r.t their approximate posterior. The conditional moments are often analytical and much easier to derive. In the most general case, we can use (fully) factorized messages so that the conditional moments can be represented by quadrature formulas. We then compute the expectation of the conditional moments via Taylor approximations when necessary. In this way, our algorithm can always conduct efficient, analytical fixed point iterations. Experiments on several popular models for which standard EP is available or unavailable demonstrate the advantages of CEP in both inference quality and computational efficiency.

The expectation-maximization (EM) algorithm has been widely used in minimizing the negative log likelihood (also known as cross entropy) of mixture models. However, little is understood about the goodness of the fixed points it converges to. In this paper, we study the regions where one component is missing in two-component mixture models, which we call one-cluster regions. We analyze the propensity of such regions to trap EM and gradient descent (GD) for mixtures of two Gaussians and mixtures of two Bernoullis. In the case of Gaussian mixtures, EM escapes one-cluster regions exponentially fast, while GD escapes them linearly fast. In the case of mixtures of Bernoullis, we find that there exist one-cluster regions that are stable for GD and therefore trap GD, but those regions are unstable for EM, allowing {EM} to escape. Those regions are local minima that appear universally in experiments and can be arbitrarily bad. This work implies that EM is less likely than GD to converge to certain bad local optima in mixture models.

We study the problem of learning sequential decision-making policies in settings with multiple state-action representations. Such settings naturally arise in many domains, such as planning (e.g., multiple integer programming formulations) and various combinatorial optimization problems (e.g., those with both integer programming and graph-based formulations). Inspired by the classical co-training framework for classification, we study the problem of co-training for policy learning. We present sufficient conditions under which learning from two views can improve upon learning from a single view alone. Motivated by these theoretical insights, we present a meta-algorithm for co-training for sequential decision making. Our framework is compatible with both reinforcement learning and imitation learning. We validate the effectiveness of our approach across a wide range of tasks, including discrete/continuous control and combinatorial optimization.

Classical causal and statistical inference methods typically assume the observed data consists of independent realizations. However, in many applications this assumption is inappropriate due to a network of dependences between units in the data. Methods for estimating causal effects have been developed in the setting where the structure of dependence between units is known exactly, but in practice there is often substantial uncertainty about the precise network structure. This is true, for example, in trial data drawn from vulnerable communities where social ties are difficult to query directly. In this paper we combine techniques from the structure learning and interference literatures in causal inference, proposing a general method for estimating causal effects under data dependence when the structure of this dependence is not known a priori. We demonstrate the utility of our method on synthetic datasets which exhibit network dependence.

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear dependencies usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis and exploits the non-stationarity of observations in order to recover the underlying sources or latent disturbances. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer the causal direction via a series of independence tests. We further propose an alternative measure of causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data.

We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-linear structural causal models that allow for cycles, latent confounders and arbitrary probability distributions. We also generalize adjustment criteria and formulas from the acyclic setting to the general one (i.e. ioSCMs). Such criteria then allow to estimate (conditional) causal effects from observational data that was (partially) gathered under selection bias and cycles. This generalizes the backdoor criterion, the selection-backdoor criterion and extensions of these to arbitrary ioSCMs. Together, our results thus enable causal reasoning in the presence of cycles, latent confounders and selection bias. Finally, we extend the ID algorithm for the identification of causal effects to ioSCMs.

Online learning, position bias, and diversified retrieval are three crucial aspects in designing ranking systems based on user clicks. One simple click model which explains the position bias is the cascade model. Many online learning variants of the cascade model have been proposed, but none so far captures diversity. Similarly, online learning to rank methods which capture diversity do not handle position bias. Motivated by these limitations, we propose a novel click model, and the associated online learning variant to address both position bias and diversified retrieval in a unified framework. Despite the objective function not being a standard submodular set function, we prove that a greedy-approach is a reasonable approximation. We then propose, CascadeLSB, an algorithm whose goal is to recommend K most attractive items from a large set of L items with the attractiveness of items being modeled as a submodular utility function. We analyze the algorithm and prove a gap-free upper bound on its n-step regret. We comprehensively evaluate CascadeLSB on synthetic and real datasets, where it outperforms all the baselines.

Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference problems such as graphical models, causal learning, feature selection and time-series analysis. While k-nearest neighbor (kNN) based estimators as well as kernel-based methods have been widely used for CMI estimation, they suffer severely from the curse of dimensionality. In this paper, we leverage advances in classifiers and generative models to design methods for CMI estimation. Specifically, we introduce an estimator for KL-Divergence based on the likelihood ratio by training a classifier to distinguish the observed joint distribution from the product distribution. We then show how to construct several CMI estimators using this basic divergence estimator by drawing ideas from conditional generative models. We demonstrate that the estimates from our proposed approaches do not degrade in performance with increasing dimension and obtain significant improvement over the widely used KSG estimator. Finally, as an application of accurate CMI estimation, we use our best estimator for conditional independence testing and achieve superior performance than the state-of-the-art tester on both simulated and real data-sets.

In this paper, we study the problem of safe online learning to re-rank, where user feedback is used to improve the quality of displayed lists. Learning to rank has traditionally been studied in two settings. In the offline setting, rankers are typically learned from relevance labels created by judges. This approach has generally become standard in industrial applications of ranking, such as search. However, this approach lacks exploration and thus is limited by the information content of the offline training data. In the online setting, an algorithm can experiment with lists and learn from feedback on them in a sequential fashion. Bandit algorithms are well-suited for this setting but they tend to learn user preferences from scratch, which results in a high initial cost of exploration. This poses an additional challenge of safe exploration in ranked lists. We propose BubbleRank, a bandit algorithm for safe re-ranking that combines the strengths of both the offline and online settings. The algorithm starts with an initial base list and improves it online by gradually exchanging higher-ranked less attractive items for lower-ranked more attractive items. We prove an upper bound on the n-step regret of BubbleRank that degrades gracefully with the quality of the initial base list. Our theoretical findings are supported by extensive experiments on a large-scale real-world click dataset.

Normalising flows (NFs) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural autoregressive flow (NAF) which is a universal approximator for density functions. Their flow is a neural network (NN) whose parameters are predicted by another NN. The latter grows quadratically with the size of the former and thus an efficient technique for parametrization is needed. We propose block neural autoregressive flow (B-NAF), a much more compact universal approximator of density functions, where we model a bijection directly using a single feed-forward network. Invertibility is ensured by carefully designing each affine transformation with block matrices that make the flow autoregressive and (strictly) monotone. We compare B-NAF to NAF and other established flows on density estimation and approximate inference for latent variable models. Our proposed flow is competitive across datasets while using orders of magnitude fewer parameters.