mtybilly/Instruct2DS huggingface dataset:
Linear Spectral Estimators and an Application to Phase Retrieval
Authors: Ramina Ghods, Andrew Lan, Tom Goldstein, Christoph Studer
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Phase retrieval refers to the problem of recovering real- or complex-valued vectors from magnitude measurements. The best-known algorithms for this problem are iterative in nature and rely on so-called spectral initializers that provide accurate initialization vectors. We propose a novel class of estimators suitable for general nonlinear measurement systems, called linear spectral estimators (LSPEs), which can be used to compute accurate initialization vectors for phase retrieval problems. The proposed LSPEs not only provide accurate initialization vectors for noisy phase retrieval systems with structured or random measurement matrices, but also enable the derivation of sharp and nonasymptotic mean-squared error bounds. We demonstrate the efficacy of LSPEs on synthetic and real-world phase retrieval problems, and we show that our estimators significantly outperform existing methods for structured measurement systems that arise in practice.
Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priors
Authors: Soumya Ghosh, Jiayu Yao, Finale Doshi-Velez
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection—even choosing the number of nodes—remains an open question. Recent work has proposed the use of a horseshoe prior over node pre-activations of a Bayesian neural network, which effectively turns off nodes that do not help explain the data. In this work, we propose several modeling and inference advances that consistently improve the compactness of the model learned while maintaining predictive performance, especially in smaller-sample settings including reinforcement learning.
Learning Maximum-A-Posteriori Perturbation Models for Structured Prediction in Polynomial Time
Authors: Asish Ghoshal, Jean Honorio
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: MAP perturbation models have emerged as a powerful framework for inference in structured prediction. Such models provide a way to efficiently sample from the Gibbs distribution and facilitate predictions that are robust to random noise. In this paper, we propose a provably polynomial time randomized algorithm for learning the parameters of perturbed MAP predictors. Our approach is based on minimizing a novel Rademacher-based generalization bound on the expected loss of a perturbed MAP predictor, which can be computed in polynomial time. We obtain conditions under which our randomized learning algorithm can guarantee generalization to unseen examples.
Robust and Scalable Models of Microbiome Dynamics
Authors: Travis Gibson, Georg Gerber
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Microbes are everywhere, including in and on our bodies, and have been shown to play key roles in a variety of prevalent human diseases. Consequently, there has been intense interest in the design of bacteriotherapies or "bugs as drugs," which are communities of bacteria administered to patients for specific therapeutic applications. Central to the design of such therapeutics is an understanding of the causal microbial interaction network and the population dynamics of the organisms. In this work we present a Bayesian nonparametric model and associated efficient inference algorithm that addresses the key conceptual and practical challenges of learning microbial dynamics from time series microbe abundance data. These challenges include high-dimensional (300+ strains of bacteria in the gut) but temporally sparse and non-uniformly sampled data; high measurement noise; and, nonlinear and physically non-negative dynamics. Our contributions include a new type of dynamical systems model for microbial dynamics based on what we term interaction modules, or learned clusters of latent variables with redundant interaction structure (reducing the expected number of interaction coefficients from O(n^2) to O((log n)^2)); a fully Bayesian formulation of the stochastic dynamical systems model that propagates measurement and latent state uncertainty throughout the model; and introduction of a temporally varying auxiliary variable technique to enable efficient inference by relaxing the hard non-negativity constraint on states. We apply our method to simulated and real data, and demonstrate the utility of our technique for system identification from limited data and gaining new biological insights into bacteriotherapy design.
Non-linear motor control by local learning in spiking neural networks
Authors: Aditya Gilra, Wulfram Gerstner
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Learning weights in a spiking neural network with hidden neurons, using local, stable and online rules, to control non-linear body dynamics is an open problem. Here, we employ a supervised scheme, Feedback-based Online Local Learning Of Weights (FOLLOW), to train a heterogeneous network of spiking neurons with hidden layers, to control a two-link arm so as to reproduce a desired state trajectory. We show that the network learns an inverse model of the non-linear dynamics, i.e. it infers from state trajectory as input to the network, the continuous-time command that produced the trajectory. Connection weights are adjusted via a local plasticity rule that involves pre-synaptic firing and post-synaptic feedback of the error in the inferred command. We propose a network architecture, termed differential feedforward, and show that it gives a lower test error than other feedforward and recurrent architectures. We demonstrate the performance of the inverse model to control a two-link arm along a desired trajectory.
Learning One Convolutional Layer with Overlapping Patches
Authors: Surbhi Goel, Adam Klivans, Raghu Meka
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches under mild conditions on the underlying distribution. We prove that our framework captures commonly used schemes from computer vision, including one-dimensional and two-dimensional “patch and stride” convolutions. Our algorithm– <em>Convotron</em>– is inspired by recent work applying isotonic regression to learning neural networks. Convotron uses a simple, iterative update rule that is stochastic in nature and tolerant to noise (requires only that the conditional mean function is a one layer convolutional network, as opposed to the realizable setting). In contrast to gradient descent, Convotron requires no special initialization or learning-rate tuning to converge to the global optimum. We also point out that learning one hidden convolutional layer with respect to a Gaussian distribution and just <em>one</em> disjoint patch $P$ (the other patches may be arbitrary) is <em>easy</em> in the following sense: Convotron can efficiently recover the hidden weight vector by updating <em>only</em> in the direction of $P$.
Visualizing and Understanding Atari Agents
Authors: Samuel Greydanus, Anurag Koul, Jonathan Dodge, Alan Fern
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: While deep reinforcement learning (deep RL) agents are effective at maximizing rewards, it is often unclear what strategies they use to do so. In this paper, we take a step toward explaining deep RL agents through a case study using Atari 2600 environments. In particular, we focus on using saliency maps to understand how an agent learns and executes a policy. We introduce a method for generating useful saliency maps and use it to show 1) what strong agents attend to, 2) whether agents are making decisions for the right or wrong reasons, and 3) how agents evolve during learning. We also test our method on non-expert human subjects and find that it improves their ability to reason about these agents. Overall, our results show that saliency information can provide significant insight into an RL agent’s decisions and learning behavior.
Learning Policy Representations in Multiagent Systems
Authors: Aditya Grover, Maruan Al-Shedivat, Jayesh Gupta, Yuri Burda, Harrison Edwards
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Modeling agent behavior is central to understanding the emergence of complex phenomena in multiagent systems. Prior work in agent modeling has largely been task-specific and driven by hand-engineering domain-specific prior knowledge. We propose a general learning framework for modeling agent behavior in any multiagent system using only a handful of interaction data. Our framework casts agent modeling as a representation learning problem. Consequently, we construct a novel objective inspired by imitation learning and agent identification and design an algorithm for unsupervised learning of representations of agent policies. We demonstrate empirically the utility of the proposed framework in (i) a challenging high-dimensional competitive environment for continuous control and (ii) a cooperative environment for communication, on supervised predictive tasks, unsupervised clustering, and policy optimization using deep reinforcement learning.
Faster Derivative-Free Stochastic Algorithm for Shared Memory Machines
Authors: Bin Gu, Zhouyuan Huo, Cheng Deng, Heng Huang
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Asynchronous parallel stochastic gradient optimization has been playing a pivotal role to solve large-scale machine learning problems in big data applications. Zeroth-order (derivative-free) methods estimate the gradient only by two function evaluations, thus have been applied to solve the problems where the explicit gradient calculations are computationally expensive or infeasible. Recently, the first asynchronous parallel stochastic zeroth-order algorithm (AsySZO) was proposed. However, its convergence rate is O(1/SQRTT) for the smooth, possibly non-convex learning problems, which is significantly slower than O(1/T) the best convergence rate of (asynchronous) stochastic gradient algorithm. To fill this gap, in this paper, we first point out the fundamental reason leading to the slow convergence rate of AsySZO, and then propose a new asynchronous stochastic zerothorder algorithm (AsySZO+). We provide a faster convergence rate O(1/bT) (b is the mini-batch size) for AsySZO+ by the rigorous theoretical analysis, which is a significant improvement over O(1/SQRTT). The experimental results on the application of ensemble learning confirm that our AsySZO+ has a faster convergence rate than the existing (asynchronous) stochastic zeroth-order algorithms.
Learning to search with MCTSnets
Authors: Arthur Guez, Theophane Weber, Ioannis Antonoglou, Karen Simonyan, Oriol Vinyals, Daan Wierstra, Remi Munos, David Silver
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Planning problems are among the most important and well-studied problems in artificial intelligence. They are most typically solved by tree search algorithms that simulate ahead into the future, evaluate future states, and back-up those evaluations to the root of a search tree. Among these algorithms, Monte-Carlo tree search (MCTS) is one of the most general, powerful and widely used. A typical implementation of MCTS uses cleverly designed rules, optimised to the particular characteristics of the domain. These rules control where the simulation traverses, what to evaluate in the states that are reached, and how to back-up those evaluations. In this paper we instead learn where, what and how to search. Our architecture, which we call an MCTSnet, incorporates simulation-based search inside a neural network, by expanding, evaluating and backing-up a vector embedding. The parameters of the network are trained end-to-end using gradient-based optimisation. When applied to small searches in the well-known planning problem Sokoban, the learned search algorithm significantly outperformed MCTS baselines.
Characterizing Implicit Bias in Terms of Optimization Geometry
Authors: Suriya Gunasekar, Jason Lee, Daniel Soudry, Nathan Srebro
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We study the bias of generic optimization methods, including Mirror Descent, Natural Gradient Descent and Steepest Descent with respect to different potentials and norms, when optimizing underdetermined linear models or separable linear classification problems. We ask the question of whether the global minimum (among the many possible global minima) reached by optimization can be characterized in terms of the potential or norm, and indecently of hyper-parameter choices, such as stepsize and momentum.
Shampoo: Preconditioned Stochastic Tensor Optimization
Authors: Vineet Gupta, Tomer Koren, Yoram Singer
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Preconditioned gradient methods are among the most general and powerful tools in optimization. However, preconditioning requires storing and manipulating prohibitively large matrices. We describe and analyze a new structure-aware preconditioning algorithm, called Shampoo, for stochastic optimization over tensor spaces. Shampoo maintains a set of preconditioning matrices, each of which operates on a single dimension, contracting over the remaining dimensions. We establish convergence guarantees in the stochastic convex setting, the proof of which builds upon matrix trace inequalities. Our experiments with state-of-the-art deep learning models show that Shampoo is capable of converging considerably faster than commonly used optimizers. Surprisingly, although it involves a more complex update rule, Shampoo’s runtime per step is comparable in practice to that of simple gradient methods such as SGD, AdaGrad, and Adam.
Latent Space Policies for Hierarchical Reinforcement Learning
Authors: Tuomas Haarnoja, Kristian Hartikainen, Pieter Abbeel, Sergey Levine
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We address the problem of learning hierarchical deep neural network policies for reinforcement learning. In contrast to methods that explicitly restrict or cripple lower layers of a hierarchy to force them to use higher-level modulating signals, each layer in our framework is trained to directly solve the task, but acquires a range of diverse strategies via a maximum entropy reinforcement learning objective. Each layer is also augmented with latent random variables, which are sampled from a prior distribution during the training of that layer. The maximum entropy objective causes these latent variables to be incorporated into the layer’s policy, and the higher level layer can directly control the behavior of the lower layer through this latent space. Furthermore, by constraining the mapping from latent variables to actions to be invertible, higher layers retain full expressivity: neither the higher layers nor the lower layers are constrained in their behavior. Our experimental evaluation demonstrates that we can improve on the performance of single-layer policies on standard benchmark tasks simply by adding additional layers, and that our method can solve more complex sparse-reward tasks by learning higher-level policies on top of high-entropy skills optimized for simple low-level objectives.
Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor
Authors: Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, Sergey Levine
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an off-policy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy. That is, to succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as Q-learning methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.
Comparison-Based Random Forests
Authors: Siavash Haghiri, Damien Garreau, Ulrike von Luxburg
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Assume we are given a set of items from a general metric space, but we neither have access to the representation of the data nor to the distances between data points. Instead, suppose that we can actively choose a triplet of items (A, B, C) and ask an oracle whether item A is closer to item B or to item C. In this paper, we propose a novel random forest algorithm for regression and classification that relies only on such triplet comparisons. In the theory part of this paper, we establish sufficient conditions for the consistency of such a forest. In a set of comprehensive experiments, we then demonstrate that the proposed random forest is efficient both for classification and regression. In particular, it is even competitive with other methods that have direct access to the metric representation of the data.
K-Beam Minimax: Efficient Optimization for Deep Adversarial Learning
Authors: Jihun Hamm, Yung-Kyun Noh
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of alternating gradient descent in minimax optimization problems due to the discontinuity of solutions of the inner maximization. To address this, we propose a new $ε$-subgradient descent algorithm that addresses this problem by simultaneously tracking $K$ candidate solutions. Practically, the algorithm can find solutions that previous saddle-point algorithms cannot find, with only a sublinear increase of complexity in $K$. We analyze the conditions under which the algorithm converges to the true solution in detail. A significant improvement in stability and convergence speed of the algorithm is observed in simple representative problems, GAN training, and domain-adaptation problems.
Candidates vs. Noises Estimation for Large Multi-Class Classification Problem
Authors: Lei Han, Yiheng Huang, Tong Zhang
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: This paper proposes a method for multi-class classification problems, where the number of classes K is large. The method, referred to as Candidates vs. Noises Estimation (CANE), selects a small subset of candidate classes and samples the remaining classes. We show that CANE is always consistent and computationally efficient. Moreover, the resulting estimator has low statistical variance approaching that of the maximum likelihood estimator, when the observed label belongs to the selected candidates with high probability. In practice, we use a tree structure with leaves as classes to promote fast beam search for candidate selection. We further apply the CANE method to estimate word probabilities in learning large neural language models. Extensive experimental results show that CANE achieves better prediction accuracy over the Noise-Contrastive Estimation (NCE), its variants and a number of the state-of-the-art tree classifiers, while it gains significant speedup compared to standard O(K) methods.
Stein Variational Gradient Descent Without Gradient
Authors: Jun Han, Qiang Liu
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Stein variational gradient decent (SVGD) has been shown to be a powerful approximate inference algorithm for complex distributions. However, the standard SVGD requires calculating the gradient of the target density and cannot be applied when the gradient is unavailable. In this work, we develop a gradient-free variant of SVGD (GF-SVGD), which replaces the true gradient with a surrogate gradient, and corrects the introduced bias by re-weighting the gradients in a proper form. We show that our GF-SVGD can be viewed as the standard SVGD with a special choice of kernel, and hence directly inherits all the theoretical properties of SVGD. We shed insights on the empirical choice of the surrogate gradient and further, propose an annealed GF-SVGD that consistently outperforms a number of recent advanced gradient-free MCMC methods in our empirical studies.
Deep Models of Interactions Across Sets
Authors: Jason Hartford, Devon Graham, Kevin Leyton-Brown, Siamak Ravanbakhsh
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We use deep learning to model interactions across two or more sets of objects, such as user–movie ratings or protein–drug bindings. The canonical representation of such interactions is a matrix (or tensor) with an exchangeability property: the encoding’s meaning is not changed by permuting rows or columns. We argue that models should hence be Permutation Equivariant (PE): constrained to make the same predictions across such permutations. We present a parameter-sharing scheme and prove that it is maximally expressive under the PE constraint. This scheme yields three benefits. First, we demonstrate performance competitive with the state of the art on multiple matrix completion benchmarks. Second, our models require a number of parameters independent of the numbers of objects and thus scale well to large datasets. Third, models can be queried about new objects that were not available at training time, but for which interactions have since been observed. We observed surprisingly good generalization performance on this matrix extrapolation task, both within domains (e.g., new users and new movies drawn from the same distribution used for training) and even across domains (e.g., predicting music ratings after training on movie ratings).
Learning Memory Access Patterns
Authors: Milad Hashemi, Kevin Swersky, Jamie Smith, Grant Ayers, Heiner Litz, Jichuan Chang, Christos Kozyrakis, Parthasarathy Ranganathan
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: The explosion in workload complexity and the recent slow-down in Moore’s law scaling call for new approaches towards efficient computing. Researchers are now beginning to use recent advances in machine learning in software optimizations; augmenting or replacing traditional heuristics and data structures. However, the space of machine learning for computer hardware architecture is only lightly explored. In this paper, we demonstrate the potential of deep learning to address the von Neumann bottleneck of memory performance. We focus on the critical problem of learning memory access patterns, with the goal of constructing accurate and efficient memory prefetchers. We relate contemporary prefetching strategies to n-gram models in natural language processing, and show how recurrent neural networks can serve as a drop-in replacement. On a suite of challenging benchmark datasets, we find that neural networks consistently demonstrate superior performance in terms of precision and recall. This work represents the first step towards practical neural-network based prefetching, and opens a wide range of exciting directions for machine learning in computer architecture research.
Fairness Without Demographics in Repeated Loss Minimization
Authors: Tatsunori Hashimoto, Megha Srivastava, Hongseok Namkoong, Percy Liang
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Machine learning models (e.g., speech recognizers) trained on average loss suffer from representation disparity—minority groups (e.g., non-native speakers) carry less weight in the training objective, and thus tend to suffer higher loss. Worse, as model accuracy affects user retention, a minority group can shrink over time. In this paper, we first show that the status quo of empirical risk minimization (ERM) amplifies representation disparity over time, which can even turn initially fair models unfair. To mitigate this, we develop an approach based on distributionally robust optimization (DRO), which minimizes the worst case risk over all distributions close to the empirical distribution. We prove that this approach controls the risk of the minority group at each time step, in the spirit of Rawlsian distributive justice, while remaining oblivious to the identity of the groups. We demonstrate that DRO prevents disparity amplification on examples where ERM fails, and show improvements in minority group user satisfaction in a real-world text autocomplete task.
Multicalibration: Calibration for the (Computationally-Identifiable) Masses
Authors: Ursula Hebert-Johnson, Michael Kim, Omer Reingold, Guy Rothblum
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We develop and study multicalibration as a new measure of fairness in machine learning that aims to mitigate inadvertent or malicious discrimination that is introduced at training time (even from ground truth data). Multicalibration guarantees meaningful (calibrated) predictions for every subpopulation that can be identified within a specified class of computations. The specified class can be quite rich; in particular, it can contain many overlapping subgroups of a protected group. We demonstrate that in many settings this strong notion of protection from discrimination is provably attainable and aligned with the goal of obtaining accurate predictions. Along the way, we present algorithms for learning a multicalibrated predictor, study the computational complexity of this task, and illustrate tight connections to the agnostic learning model.
Recurrent Predictive State Policy Networks
Authors: Ahmed Hefny, Zita Marinho, Wen Sun, Siddhartha Srinivasa, Geoffrey Gordon
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: 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.
Learning unknown ODE models with Gaussian processes
Authors: Markus Heinonen, Cagatay Yildiz, Henrik Mannerström, Jukka Intosalmi, Harri Lähdesmäki
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model’s capabilities to infer dynamics from sparse data and to simulate the system forward into future.
Orthogonal Recurrent Neural Networks with Scaled Cayley Transform
Authors: Kyle Helfrich, Devin Willmott, Qiang Ye
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients. Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases, exceed the capabilities of Long Short-Term Memory networks (LSTMs). We propose a simpler and novel update scheme to maintain orthogonal recurrent weight matrices without using complex valued matrices. This is done by parametrizing with a skew-symmetric matrix using the Cayley transform; such a parametrization is unable to represent matrices with negative one eigenvalues, but this limitation is overcome by scaling the recurrent weight matrix by a diagonal matrix consisting of ones and negative ones. The proposed training scheme involves a straightforward gradient calculation and update step. In several experiments, the proposed scaled Cayley orthogonal recurrent neural network (scoRNN) achieves superior results with fewer trainable parameters than other unitary RNNs.
Fast Bellman Updates for Robust MDPs
Authors: Chin Pang Ho, Marek Petrik, Wolfram Wiesemann
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We describe two efficient, and exact, algorithms for computing Bellman updates in robust Markov decision processes (MDPs). The first algorithm uses a homotopy continuation method to compute updates for L1-constrained s,a-rectangular ambiguity sets. It runs in quasi-linear time for plain L1-norms and also generalizes to weighted L1-norms. The second algorithm uses bisection to compute updates for robust MDPs with s-rectangular ambiguity sets. This algorithm, when combined with the homotopy method, also has a quasi-linear runtime. Unlike previous methods, our algorithms compute the primal solution in addition to the optimal objective value, which makes them useful in policy iteration methods. Our experimental results indicate that the proposed methods are over 1,000 times faster than Gurobi, a state-of-the-art commercial optimization package, for small instances, and the performance gap grows considerably with problem size.
CyCADA: Cycle-Consistent Adversarial Domain Adaptation
Authors: Judy Hoffman, Eric Tzeng, Taesung Park, Jun-Yan Zhu, Phillip Isola, Kate Saenko, Alexei Efros, Trevor Darrell
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Domain adaptation is critical for success in new, unseen environments. Adversarial adaptation models have shown tremendous progress towards adapting to new environments by focusing either on discovering domain invariant representations or by mapping between unpaired image domains. While feature space methods are difficult to interpret and sometimes fail to capture pixel-level and low-level domain shifts, image space methods sometimes fail to incorporate high level semantic knowledge relevant for the end task. We propose a model which adapts between domains using both generative image space alignment and latent representation space alignment. Our approach, Cycle-Consistent Adversarial Domain Adaptation (CyCADA), guides transfer between domains according to a specific discriminatively trained task and avoids divergence by enforcing consistency of the relevant semantics before and after adaptation. We evaluate our method on a variety of visual recognition and prediction settings, including digit classification and semantic segmentation of road scenes, advancing state-of-the-art performance for unsupervised adaptation from synthetic to real world driving domains.
Sound Abstraction and Decomposition of Probabilistic Programs
Authors: Steven Holtzen, Guy Van den Broeck, Todd Millstein
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Probabilistic programming languages are a flexible tool for specifying statistical models, but this flexibility comes at the cost of efficient analysis. It is currently difficult to compactly represent the subtle independence properties of a probabilistic program, and exploit independence properties to decompose inference. Classical graphical model abstractions do capture some properties of the underlying distribution, enabling inference algorithms to operate at the level of the graph topology. However, we observe that graph-based abstractions are often too coarse to capture interesting properties of programs. We propose a form of sound abstraction for probabilistic programs wherein the abstractions are themselves simplified programs. We provide a theoretical foundation for these abstractions, as well as an algorithm to generate them. Experimentally, we also illustrate the practical benefits of our framework as a tool to decompose probabilistic program inference.
Gradient Primal-Dual Algorithm Converges to Second-Order Stationary Solution for Nonconvex Distributed Optimization Over Networks
Authors: Mingyi Hong, Meisam Razaviyayn, Jason Lee
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: In this work, we study two first-order primal-dual based algorithms, the Gradient Primal-Dual Algorithm (GPDA) and the Gradient Alternating Direction Method of Multipliers (GADMM), for solving a class of linearly constrained non-convex optimization problems. We show that with random initialization of the primal and dual variables, both algorithms are able to compute second-order stationary solutions (ss2) with probability one. This is the first result showing that primal-dual algorithm is capable of finding ss2 when only using first-order information; it also extends the existing results for first-order, but primal-only algorithms. An important implication of our result is that it also gives rise to the first global convergence result to the ss2, for two classes of unconstrained distributed non-convex learning problems over multi-agent networks.
Variational Bayesian dropout: pitfalls and fixes
Authors: Jiri Hron, Alex Matthews, Zoubin Ghahramani
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the algorithm. We show that the proposed framework suffers from several issues; from undefined or pathological behaviour of the true posterior related to use of improper priors, to an ill-defined variational objective due to singularity of the approximating distribution relative to the true posterior. Our analysis of the improper log uniform prior used in variational Gaussian dropout suggests the pathologies are generally irredeemable, and that the algorithm still works only because the variational formulation annuls some of the pathologies. To address the singularity issue, we proffer Quasi-KL (QKL) divergence, a new approximate inference objective for approximation of high-dimensional distributions. We show that motivations for variational Bernoulli dropout based on discretisation and noise have QKL as a limit. Properties of QKL are studied both theoretically and on a simple practical example which shows that the QKL-optimal approximation of a full rank Gaussian with a degenerate one naturally leads to the Principal Component Analysis solution.
Does Distributionally Robust Supervised Learning Give Robust Classifiers?
Authors: Weihua Hu, Gang Niu, Issei Sato, Masashi Sugiyama
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Distributionally Robust Supervised Learning (DRSL) is necessary for building reliable machine learning systems. When machine learning is deployed in the real world, its performance can be significantly degraded because test data may follow a different distribution from training data. DRSL with f-divergences explicitly considers the worst-case distribution shift by minimizing the adversarially reweighted training loss. In this paper, we analyze this DRSL, focusing on the classification scenario. Since the DRSL is explicitly formulated for a distribution shift scenario, we naturally expect it to give a robust classifier that can aggressively handle shifted distributions. However, surprisingly, we prove that the DRSL just ends up giving a classifier that exactly fits the given training distribution, which is too pessimistic. This pessimism comes from two sources: the particular losses used in classification and the fact that the variety of distributions to which the DRSL tries to be robust is too wide. Motivated by our analysis, we propose simple DRSL that overcomes this pessimism and empirically demonstrate its effectiveness.
Dissipativity Theory for Accelerating Stochastic Variance Reduction: A Unified Analysis of SVRG and Katyusha Using Semidefinite Programs
Authors: Bin Hu, Stephen Wright, Laurent Lessard
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Techniques for reducing the variance of gradient estimates used in stochastic programming algorithms for convex finite-sum problems have received a great deal of attention in recent years. By leveraging dissipativity theory from control, we provide a new perspective on two important variance-reduction algorithms: SVRG and its direct accelerated variant Katyusha. Our perspective provides a physically intuitive understanding of the behavior of SVRG-like methods via a principle of energy conservation. The tools discussed here allow us to automate the convergence analysis of SVRG-like methods by capturing their essential properties in small semidefinite programs amenable to standard analysis and computational techniques. Our approach recovers existing convergence results for SVRG and Katyusha and generalizes the theory to alternative parameter choices. We also discuss how our approach complements the linear coupling technique. Our combination of perspectives leads to a better understanding of accelerated variance-reduced stochastic methods for finite-sum problems.
Near Optimal Frequent Directions for Sketching Dense and Sparse Matrices
Authors: Zengfeng Huang
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Given a large matrix $Aıne̊al^n\times d$, we consider the problem of computing a sketch matrix $Bın\ål^\ell\times d$ which is significantly smaller than but still well approximates $A$. We are interested in minimizing the <em>covariance error</em> $\normA^TA-B^TB_2.$We consider the problems in the streaming model, where the algorithm can only make one pass over the input with limited working space. The popular Frequent Directions algorithm of Liberty (2013) and its variants achieve optimal space-error tradeoff. However, whether the running time can be improved remains an unanswered question.In this paper, we almost settle the time complexity of this problem. In particular, we provide new space-optimal algorithms with faster running times. Moreover, we also show that the running times of our algorithms are near-optimal unless the state-of-the-art running time of matrix multiplication can be improved significantly.
Learning Deep ResNet Blocks Sequentially using Boosting Theory
Authors: Furong Huang, Jordan Ash, John Langford, Robert Schapire
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We prove a <em>multi-channel telescoping sum boosting</em> theory for the ResNet architectures which simultaneously creates a new technique for boosting over features (in contrast with labels) and provides a new algorithm for ResNet-style architectures. Our proposed training algorithm, <em>BoostResNet</em>, is particularly suitable in non-differentiable architectures. Our method only requires the relatively inexpensive sequential training of $T$ “shallow ResNets”. We prove that the training error decays exponentially with the depth $T$ if the weak module classifiers that we train perform slightly better than some weak baseline. In other words, we propose a weak learning condition and prove a boosting theory for ResNet under the weak learning condition. A generalization error bound based on margin theory is proved and suggests that ResNet could be resistant to overfitting using a network with $l_1$ norm bounded weights.
Learning Hidden Markov Models from Pairwise Co-occurrences with Application to Topic Modeling
Authors: Kejun Huang, Xiao Fu, Nicholas Sidiropoulos
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We present a new algorithm for identifying the transition and emission probabilities of a hidden Markov model (HMM) from the emitted data. Expectation-maximization becomes computationally prohibitive for long observation records, which are often required for identification. The new algorithm is particularly suitable for cases where the available sample size is large enough to accurately estimate second-order output probabilities, but not higher-order ones. We show that if one is only able to obtain a reliable estimate of the pairwise co-occurrence probabilities of the emissions, it is still possible to uniquely identify the HMM if the emission probability is <em>sufficiently scattered</em>. We apply our method to hidden topic Markov modeling, and demonstrate that we can learn topics with higher quality if documents are modeled as observations of HMMs sharing the same emission (topic) probability, compared to the simple but widely used bag-of-words model.
Neural Autoregressive Flows
Authors: Chin-Wei Huang, David Krueger, Alexandre Lacoste, Aaron Courville
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Normalizing flows and autoregressive models have been successfully combined to produce state-of-the-art results in density estimation, via Masked Autoregressive Flows (MAF) (Papamakarios et al., 2017), and to accelerate state-of-the-art WaveNet-based speech synthesis to 20x faster than real-time (Oord et al., 2017), via Inverse Autoregressive Flows (IAF) (Kingma et al., 2016). We unify and generalize these approaches, replacing the (conditionally) affine univariate transformations of MAF/IAF with a more general class of invertible univariate transformations expressed as monotonic neural networks. We demonstrate that the proposed neural autoregressive flows (NAF) are universal approximators for continuous probability distributions, and their greater expressivity allows them to better capture multimodal target distributions. Experimentally, NAF yields state-of-the-art performance on a suite of density estimation tasks and outperforms IAF in variational autoencoders trained on binarized MNIST.
Topological mixture estimation
Authors: Steve Huntsman
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: We introduce topological mixture estimation, a completely nonparametric and computationally efficient solution to the problem of estimating a one-dimensional mixture with generic unimodal components. We repeatedly perturb the unimodal decomposition of Baryshnikov and Ghrist to produce a topologically and information-theoretically optimal unimodal mixture. We also detail a smoothing process that optimally exploits topological persistence of the unimodal category in a natural way when working directly with sample data. Finally, we illustrate these techniques through examples.
Decoupled Parallel Backpropagation with Convergence Guarantee
Authors: Zhouyuan Huo, Bin Gu, qian Yang, Heng Huang
Published in: Proceedings of the 35th International Conference on Machine Learning (Main Conference Track), 2018

Abstract: Backpropagation algorithm is indispensable for the training of feedforward neural networks. It requires propagating error gradients sequentially from the output layer all the way back to the input layer. The backward locking in backpropagation algorithm constrains us from updating network layers in parallel and fully leveraging the computing resources. Recently, several algorithms have been proposed for breaking the backward locking. However, their performances degrade seriously when networks are deep. In this paper, we propose decoupled parallel backpropagation algorithm for deep learning optimization with convergence guarantee. Firstly, we decouple the backpropagation algorithm using delayed gradients, and show that the backward locking is removed when we split the networks into multiple modules. Then, we utilize decoupled parallel backpropagation in two stochastic methods and prove that our method guarantees convergence to critical points for the non-convex problem. Finally, we perform experiments for training deep convolutional neural networks on benchmark datasets. The experimental results not only confirm our theoretical analysis, but also demonstrate that the proposed method can achieve significant speedup without loss of accuracy.