mtybilly/Instruct2DS huggingface dataset:
Differential Geometric Regularization for Supervised Learning of Classifiers
Authors: Qinxun Bai, Steven Rosenberg, Zheng Wu, Stan Sclaroff
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to an estimator of the class probability P(y|ěc x). The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces rapid local oscillations and hence large volume of the estimator. This technique can be applied to regularize any classification function that satisfies two requirements: firstly, an estimator of the class probability can be obtained; secondly, first and second derivatives of the class probability estimator can be calculated. In experiments, we apply our regularization technique to standard loss functions for classification, our RBF-based implementation compares favorably to widely used regularization methods for both binary and multiclass classification.
Exploiting Cyclic Symmetry in Convolutional Neural Networks
Authors: Sander Dieleman, Jeffrey De Fauw, Koray Kavukcuoglu
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data. Encoding these properties into the network architecture, as we are already used to doing for translation equivariance by using convolutional layers, could result in a more efficient use of the parameter budget by relieving the model from learning them. We introduce four operations which can be inserted into neural network models as layers, and which can be combined to make these models partially equivariant to rotations. They also enable parameter sharing across different orientations. We evaluate the effect of these architectural modifications on three datasets which exhibit rotational symmetry and demonstrate improved performance with smaller models.
Graying the black box: Understanding DQNs
Authors: Tom Zahavy, Nir Ben-Zrihem, Shie Mannor
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In recent years there is a growing interest in using deep representations for reinforcement learning. In this paper, we present a methodology and tools to analyze Deep Q-networks (DQNs) in a non-blind matter. Using our tools we reveal that the features learned by DQNs aggregate the state space in a hierarchical fashion, explaining its success. Moreover we are able to understand and describe the policies learned by DQNs for three different Atari2600 games and suggest ways to interpret, debug and optimize of deep neural networks in Reinforcement Learning.
The Sum-Product Theorem: A Foundation for Learning Tractable Models
Authors: Abram Friesen, Pedro Domingos
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even when an arbitrary number of hidden layers are present. In this paper, we generalize this result to a much broader set of learning problems: all those where inference consists of summing a function over a semiring. This includes satisfiability, constraint satisfaction, optimization, integration, and others. In any semiring, for summation to be tractable it suffices that the factors of every product have disjoint scopes. This unifies and extends many previous results in the literature. Enforcing this condition at learning time thus ensures that the learned models are tractable. We illustrate the power and generality of this approach by applying it to a new type of structured prediction problem: learning a nonconvex function that can be globally optimized in polynomial time. We show empirically that this greatly outperforms the standard approach of learning without regard to the cost of optimization.
Pareto Frontier Learning with Expensive Correlated Objectives
Authors: Amar Shah, Zoubin Ghahramani
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: There has been a surge of research interest in developing tools and analysis for Bayesian optimization, the task of finding the global maximizer of an unknown, expensive function through sequential evaluation using Bayesian decision theory. However, many interesting problems involve optimizing multiple, expensive to evaluate objectives simultaneously, and relatively little research has addressed this setting from a Bayesian theoretic standpoint. A prevailing choice when tackling this problem, is to model the multiple objectives as being independent, typically for ease of computation. In practice, objectives are correlated to some extent. In this work, we incorporate the modelling of inter-task correlations, developing an approximation to overcome intractable integrals. We illustrate the power of modelling dependencies between objectives on a range of synthetic and real world multi-objective optimization problems.
Asynchronous Methods for Deep Reinforcement Learning
Authors: Volodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim Harley, David Silver, Koray Kavukcuoglu
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose a conceptually simple and lightweight framework for deep reinforcement learning that uses asynchronous gradient descent for optimization of deep neural network controllers. We present asynchronous variants of four standard reinforcement learning algorithms and show that parallel actor-learners have a stabilizing effect on training allowing all four methods to successfully train neural network controllers. The best performing method, an asynchronous variant of actor-critic, surpasses the current state-of-the-art on the Atari domain while training for half the time on a single multi-core CPU instead of a GPU. Furthermore, we show that asynchronous actor-critic succeeds on a wide variety of continuous motor control problems as well as on a new task of navigating random 3D mazes using a visual input.
A Simple and Strongly-Local Flow-Based Method for Cut Improvement
Authors: Nate Veldt, David Gleich, Michael Mahoney
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Many graph-based learning problems can be cast as finding a good set of vertices nearby a seed set, and a powerful methodology for these problems is based on minimum cuts and maximum flows. We introduce and analyze a new method for locally-biased graph-based learning called SimpleLocal, which finds good conductance cuts near a set of seed vertices. An important feature of our algorithm is that it is strongly-local, meaning it does not need to explore the entire graph to find cuts that are locally optimal. This method is related to other strongly-local flow-based methods, but it enables a simple implementation. We also show how it achieves localization through an implicit l1-norm penalty term. As a flow-based method, our algorithm exhibits several advantages in terms of cut optimality and accurate identification of target regions in a graph. We demonstrate the power of SimpleLocal solving segmentation problems on a 467 million edge graph based on an MRI scan.
Nonlinear Statistical Learning with Truncated Gaussian Graphical Models
Authors: Qinliang Su, Xuejun Liao, Changyou Chen, Lawrence Carin
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal model. We show that the variables in the marginal model are non-Gaussian distributed and their expected relations are nonlinear. We use expectation-maximization to break the inference of the nonlinear model into a sequence of TGGM inference problems, each of which is efficiently solved by using the properties and numerical methods of multivariate Gaussian distributions. We use the TGGM to design models for nonlinear regression and classification, with the performances of these models demonstrated on extensive benchmark datasets and compared to state-of-the-art competing results.
Barron and Cover's Theory in Supervised Learning and its Application to Lasso
Authors: Masanori Kawakita, Jun’ichi Takeuchi
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study Barron and Cover’s theory (BC theory) in supervised learning. The original BC theory can be applied to supervised learning only approximately and limitedly. Though Barron (2008) and Chatterjee and Barron (2014) succeeded in removing the approximation, their idea cannot be essentially applied to supervised learning in general. By solving this issue, we propose an extension of BC theory to supervised learning. The extended theory has several advantages inherited from the original BC theory. First, it holds for finite sample number n. Second, it requires remarkably few assumptions. Third, it gives a justification of the MDL principle in supervised learning. We also derive new risk and regret bounds of lasso with random design as its application. The derived risk bound hold for any finite n without boundedness of features in contrast to past work. Behavior of the regret bound is investigated by numerical simulations. We believe that this is the first extension of BC theory to general supervised learning without approximation.
Nonparametric Canonical Correlation Analysis
Authors: Tomer Michaeli, Weiran Wang, Karen Livescu
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep neural network methods. These approaches seek maximally correlated projections among families of functions, which the user specifies (by choosing a kernel or neural network structure), and are computationally demanding. Interestingly, the theory of nonlinear CCA, without functional restrictions, had been studied in the population setting by Lancaster already in the 1950s, but these results have not inspired practical algorithms. We revisit Lancaster’s theory to devise a practical algorithm for nonparametric CCA (NCCA). Specifically, we show that the solution can be expressed in terms of the singular value decomposition of a certain operator associated with the joint density of the views. Thus, by estimating the population density from data, NCCA reduces to solving an eigenvalue system, superficially like kernel CCA but, importantly, without requiring the inversion of any kernel matrix. We also derive a partially linear CCA (PLCCA) variant in which one of the views undergoes a linear projection while the other is nonparametric. Using a kernel density estimate based on a small number of nearest neighbors, our NCCA and PLCCA algorithms are memory-efficient, often run much faster, and perform better than kernel CCA and comparable to deep CCA.
BISTRO: An Efficient Relaxation-Based Method for Contextual Bandits
Authors: Alexander Rakhlin, Karthik Sridharan
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled data to make the problem computationally simple. When the ERM problem itself is computationally hard, we extend the approach by employing multiplicative approximation algorithms for the ERM. The integrality gap of the relaxation only enters in the regret bound rather than the benchmark. Finally, we show that the adversarial version of the contextual bandit problem is learnable (and efficient) whenever the full-information supervised online learning problem has a non-trivial regret bound (and efficient).
Associative Long Short-Term Memory
Authors: Ivo Danihelka, Greg Wayne, Benigno Uria, Nal Kalchbrenner, Alex Graves
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We investigate a new method to augment recurrent neural networks with extra memory without increasing the number of network parameters. The system has an associative memory based on complex-valued vectors and is closely related to Holographic Reduced Representations and Long Short-Term Memory networks. Holographic Reduced Representations have limited capacity: as they store more information, each retrieval becomes noisier due to interference. Our system in contrast creates redundant copies of stored information, which enables retrieval with reduced noise. Experiments demonstrate faster learning on multiple memorization tasks.
Dueling Network Architectures for Deep Reinforcement Learning
Authors: Ziyu Wang, Tom Schaul, Matteo Hessel, Hado Hasselt, Marc Lanctot, Nando Freitas
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In recent years there have been many successes of using deep representations in reinforcement learning. Still, many of these applications use conventional architectures, such as convolutional networks, LSTMs, or auto-encoders. In this paper, we present a new neural network architecture for model-free reinforcement learning. Our dueling network represents two separate estimators: one for the state value function and one for the state-dependent action advantage function. The main benefit of this factoring is to generalize learning across actions without imposing any change to the underlying reinforcement learning algorithm. Our results show that this architecture leads to better policy evaluation in the presence of many similar-valued actions. Moreover, the dueling architecture enables our RL agent to outperform the state-of-the-art on the Atari 2600 domain.
Persistence weighted Gaussian kernel for topological data analysis
Authors: Genki Kusano, Yasuaki Hiraoka, Kenji Fukumizu
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy topological properties. This paper proposes a kernel method on persistence diagrams to develop a statistical framework in TDA. The proposed kernel satisfies the stability property and provides explicit control on the effect of persistence. Furthermore, the method allows a fast approximation technique. The method is applied into practical data on proteins and oxide glasses, and the results show the advantage of our method compared to other relevant methods on persistence diagrams.
Learning Convolutional Neural Networks for Graphs
Authors: Mathias Niepert, Mohamed Ahmed, Konstantin Kutzkov
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.
Persistent RNNs: Stashing Recurrent Weights On-Chip
Authors: Greg Diamos, Shubho Sengupta, Bryan Catanzaro, Mike Chrzanowski, Adam Coates, Erich Elsen, Jesse Engel, Awni Hannun, Sanjeev Satheesh
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: This paper introduces a new technique for mapping Deep Recurrent Neural Networks (RNN) efficiently onto GPUs. We show how it is possi- ble to achieve substantially higher computational throughput at low mini-batch sizes than direct implementations of RNNs based on matrix multiplications. The key to our approach is the use of persistent computational kernels that exploit the GPU’s inverted memory hierarchy to reuse network weights over multiple timesteps. Our initial implementation sustains 2.8 TFLOP/s at a mini-batch size of 4 on an NVIDIA TitanX GPU. This provides a 16x reduction in activation memory footprint, enables model training with 12x more parameters on the same hardware, allows us to strongly scale RNN training to 128 GPUs, and allows us to efficiently explore end-to-end speech recognition models with over 100 layers.
Recurrent Orthogonal Networks and Long-Memory Tasks
Authors: Mikael Henaff, Arthur Szlam, Yann LeCun
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Although RNNs have been shown to be power- ful tools for processing sequential data, finding architectures or optimization strategies that al- low them to model very long term dependencies is still an active area of research. In this work, we carefully analyze two synthetic datasets orig- inally outlined in (Hochreiter & Schmidhuber, 1997) which are used to evaluate the ability of RNNs to store information over many time steps. We explicitly construct RNN solutions to these problems, and using these constructions, illumi- nate both the problems themselves and the way in which RNNs store different types of information in their hidden states. These constructions fur- thermore explain the success of recent methods that specify unitary initializations or constraints on the transition matrices.
The Arrow of Time in Multivariate Time Series
Authors: Stefan Bauer, Bernhard Schölkopf, Jonas Peters
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We prove that a time series satisfying a (linear) multivariate autoregressive moving average (VARMA) model satisfies the same model assumption in the reversed time direction, too, if all innovations are normally distributed. This reversibility breaks down if the innovations are non-Gaussian. This means that under the assumption of a VARMA process with non-Gaussian noise, the arrow of time becomes detectable. Our work thereby provides a theoretic justification of an algorithm that has been used for inferring the direction of video snippets. We present a slightly modified practical algorithm that estimates the time direction for a given sample and prove its consistency. We further investigate how the performance of the algorithm depends on sample size, number of dimensions of the time series and the order of the process. An application to real world data from economics shows that considering multivariate processes instead of univariate processes can be beneficial for estimating the time direction. Our result extends earlier work on univariate time series. It relates to the concept of causal inference, where recent methods exploit non-Gaussianity of the error terms for causal structure learning.
Mixture Proportion Estimation via Kernel Embeddings of Distributions
Authors: Harish Ramaswamy, Clayton Scott, Ambuj Tewari
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning" problems like learning with positive and unlabelled samples, learning with label noise, anomaly detection and crowdsourcing. While there have been several methods proposed to solve this problem, to the best of our knowledge no efficient algorithm with a proven convergence rate towards the true proportion exists for this problem. We fill this gap by constructing a provably correct algorithm for MPE, and derive convergence rates under certain assumptions on the distribution. Our method is based on embedding distributions onto an RKHS, and implementing it only requires solving a simple convex quadratic programming problem a few times. We run our algorithm on several standard classification datasets, and demonstrate that it performs comparably to or better than other algorithms on most datasets.
Fast DPP Sampling for Nystrom with Application to Kernel Methods
Authors: Chengtao Li, Stefanie Jegelka, Suvrit Sra
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The Nystrom method has long been popular for scaling up kernel methods. Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected. We study landmark selection for Nystrom using Determinantal Point Processes (DPPs), discrete probability models that allow tractable generation of diverse samples. We prove that landmarks selected via DPPs guarantee bounds on approximation errors; subsequently, we analyze implications for kernel ridge regression. Contrary to prior reservations due to cubic complexity of DPP sampling, we show that (under certain conditions) Markov chain DPP sampling requires only linear time in the size of the data. We present several empirical results that support our theoretical analysis, and demonstrate the superior performance of DPP-based landmark selection compared with existing approaches.
Complex Embeddings for Simple Link Prediction
Authors: Théo Trouillon, Johannes Welbl, Sebastian Riedel, Eric Gaussier, Guillaume Bouchard
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.
Interactive Bayesian Hierarchical Clustering
Authors: Sharad Vikram, Sanjoy Dasgupta
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Clustering is a powerful tool in data analysis, but it is often difficult to find a grouping that aligns with a user’s needs. To address this, several methods incorporate constraints obtained from users into clustering algorithms, but unfortunately do not apply to hierarchical clustering. We design an interactive Bayesian algorithm that incorporates user interaction into hierarchical clustering while still utilizing the geometry of the data by sampling a constrained posterior distribution over hierarchies. We also suggest several ways to intelligently query a user. The algorithm, along with the querying schemes, shows promising results on real data.
A Convolutional Attention Network for Extreme Summarization of Source Code
Authors: Miltiadis Allamanis, Hao Peng, Charles Sutton
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Attention mechanisms in neural networks have proved useful for problems in which the input and output do not have fixed dimension. Often there exist features that are locally translation invariant and would be valuable for directing the model’s attention, but previous attentional architectures are not constructed to learn such features specifically. We introduce an attentional neural network that employs convolution on the input tokens to detect local time-invariant and long-range topical attention features in a context-dependent way. We apply this architecture to the problem of extreme summarization of source code snippets into short, descriptive function name-like summaries. Using those features, the model sequentially generates a summary by marginalizing over two attention mechanisms: one that predicts the next summary token based on the attention weights of the input tokens and another that is able to copy a code token as-is directly into the summary. We demonstrate our convolutional attention neural network’s performance on 10 popular Java projects showing that it achieves better performance compared to previous attentional mechanisms.
How to Fake Multiply by a Gaussian Matrix
Authors: Michael Kapralov, Vamsi Potluru, David Woodruff
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Have you ever wanted to multiply an n \times d matrix X, with n ≫d, on the left by an m \times n matrix \tilde G of i.i.d. Gaussian random variables, but could not afford to do it because it was too slow? In this work we propose a new randomized m \times n matrix T, for which one can compute T ⋅X in only O(nnz(X)) + \tilde O(m^1.5 ⋅d^3) time, for which the total variation distance between the distributions T ⋅X and \tilde G ⋅X is as small as desired, i.e., less than any positive constant. Here nnz(X) denotes the number of non-zero entries of X. Assuming nnz(X) ≫m^1.5 ⋅d^3, this is a significant savings over the naïve O(nnz(X) m) time to compute \tilde G ⋅X. Moreover, since the total variation distance is small, we can provably use T ⋅X in place of \tilde G ⋅X in any application and have the same guarantees as if we were using \tilde G ⋅X, up to a small positive constant in error probability. We apply this transform to nonnegative matrix factorization (NMF) and support vector machines (SVM).
Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing
Authors: Marco Gaboardi, Hyun Lim, Ryan Rogers, Salil Vadhan
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about individuals, such as medical information. Thus it is important to design statistical tests that guarantee the privacy of subjects in the data. In this work, we study hypothesis testing subject to differential privacy, specifically chi-squared tests for goodness of fit for multinomial data and independence between two categorical variables.
Pliable Rejection Sampling
Authors: Akram Erraqabi, Michal Valko, Alexandra Carpentier, Odalric Maillard
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without performance guarantees. In this paper, we present pliable rejection sampling (PRS), a new approach to rejection sampling, where we learn the sampling proposal using a kernel estimator. Since our method builds on rejection sampling, the samples obtained are with high probability i.i.d. and distributed according to f. Moreover, PRS comes with a guarantee on the number of accepted samples.
Differentially Private Policy Evaluation
Authors: Borja Balle, Maziar Gomrokchi, Doina Precup
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present the first differentially private algorithms for reinforcement learning, which apply to the task of evaluating a fixed policy. We establish two approaches for achieving differential privacy, provide a theoretical analysis of the privacy and utility of the two algorithms, and show promising results on simple empirical examples.
Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning
Authors: Philip Thomas, Emma Brunskill
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In this paper we present a new way of predicting the performance of a reinforcement learning policy given historical data that may have been generated by a different policy. The ability to evaluate a policy from historical data is important for applications where the deployment of a bad policy can be dangerous or costly. We show empirically that our algorithm produces estimates that often have orders of magnitude lower mean squared error than existing methods—it makes more efficient use of the available data. Our new estimator is based on two advances: an extension of the doubly robust estimator (Jiang & Li, 2015), and a new way to mix between model based and importance sampling based estimates.
Discrete Deep Feature Extraction: A Theory and New Architectures
Authors: Thomas Wiatowski, Michael Tschannen, Aleksandar Stanic, Philipp Grohs, Helmut Boelcskei
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made—for the continuous-time case—in Mallat, 2012, and Wiatowski and Bölcskei, 2015. This paper considers the discrete case, introduces new convolutional neural network architectures, and proposes a mathematical framework for their analysis. Specifically, we establish deformation and translation sensitivity results of local and global nature, and we investigate how certain structural properties of the input signal are reflected in the corresponding feature vectors. Our theory applies to general filters and general Lipschitz-continuous non-linearities and pooling operators. Experiments on handwritten digit classification and facial landmark detection—including feature importance evaluation—complement the theoretical findings.
Efficient Algorithms for Adversarial Contextual Learning
Authors: Vasilis Syrgkanis, Akshay Krishnamurthy, Robert Schapire
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We provide the first oracle efficient sublinear regret algorithms for adversarial versions of the contextual bandit problem. In this problem, the learner repeatedly makes an action on the basis of a context and receives reward for the chosen action, with the goal of achieving reward competitive with a large class of policies. We analyze two settings: i) in the transductive setting the learner knows the set of contexts a priori, ii) in the small separator setting, there exists a small set of contexts such that any two policies behave differently on one of the contexts in the set. Our algorithms fall into the Follow-The-Perturbed-Leader family (Kalai and Vempala, 2005) and achieve regret O(T^3/4\sqrtKłog(N)) in the transductive setting and O(T^2/3 d^3/4 K\sqrtłog(N)) in the separator setting, where T is the number of rounds, K is the number of actions, N is the number of baseline policies, and d is the size of the separator. We actually solve the more general adversarial contextual semi-bandit linear optimization problem, whilst in the full information setting we address the even more general contextual combinatorial optimization. We provide several extensions and implications of our algorithms, such as switching regret and efficient learning with predictable sequences.
Training Deep Neural Networks via Direct Loss Minimization
Authors: Yang Song, Alexander Schwing,  Richard, Raquel Urtasun
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Supervised training of deep neural nets typically relies on minimizing cross-entropy. However, in many domains, we are interested in performing well on metrics specific to the application. In this paper we propose a direct loss minimization approach to train deep neural networks, which provably minimizes the application-specific loss function. This is often non-trivial, since these functions are neither smooth nor decomposable and thus are not amenable to optimization with standard gradient-based methods. We demonstrate the effectiveness of our approach in the context of maximizing average precision for ranking problems. Towards this goal, we develop a novel dynamic programming algorithm that can efficiently compute the weight updates. Our approach proves superior to a variety of baselines in the context of action classification and object detection, especially in the presence of label noise.
Sequence to Sequence Training of CTC-RNNs with Partial Windowing
Authors: Kyuyeon Hwang, Wonyong Sung
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Connectionist temporal classification (CTC) based supervised sequence training of recurrent neural networks (RNNs) has shown great success in many machine learning areas including end-to-end speech and handwritten character recognition. For the CTC training, however, it is required to unroll (or unfold) the RNN by the length of an input sequence. This unrolling requires a lot of memory and hinders a small footprint implementation of online learning or adaptation. Furthermore, the length of training sequences is usually not uniform, which makes parallel training with multiple sequences inefficient on shared memory models such as graphics processing units (GPUs). In this work, we introduce an expectation-maximization (EM) based online CTC algorithm that enables unidirectional RNNs to learn sequences that are longer than the amount of unrolling. The RNNs can also be trained to process an infinitely long input sequence without pre-segmentation or external reset. Moreover, the proposed approach allows efficient parallel training on GPUs. Our approach achieves 20.7% phoneme error rate (PER) on the very long input sequence that is generated by concatenating all 192 utterances in the TIMIT core test set. In the end-to-end speech recognition task on the Wall Street Journal corpus, a network can be trained with only 64 times of unrolling with little performance loss.
Variational Inference for Monte Carlo Objectives
Authors: Andriy Mnih, Danilo Rezende
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood, using samples from the variational posterior to compute the required gradients. Recently, Burda et al. (2016) have derived a tighter lower bound using a multi-sample importance sampling estimate of the likelihood and showed that optimizing it yields models that use more of their capacity and achieve higher likelihoods. This development showed the importance of such multi-sample objectives and explained the success of several related approaches. We extend the multi-sample approach to discrete latent variables and analyze the difficulty encountered when estimating the gradients involved. We then develop the first unbiased gradient estimator designed for importance-sampled objectives and evaluate it at training generative and structured output prediction models. The resulting estimator, which is based on low-variance per-sample learning signals, is both simpler and more effective than the NVIL estimator proposed for the single-sample variational objective, and is competitive with the currently used biased estimators.
Hierarchical Decision Making In Electricity Grid Management
Authors: Gal Dalal, Elad Gilboa, Shie Mannor
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The power grid is a complex and vital system that necessitates careful reliability management. Managing the grid is a difficult problem with multiple time scales of decision making and stochastic behavior due to renewable energy generations, variable demand and unplanned outages. Solving this problem in the face of uncertainty requires a new methodology with tractable algorithms. In this work, we introduce a new model for hierarchical decision making in complex systems. We apply reinforcement learning (RL) methods to learn a proxy, i.e., a level of abstraction, for real-time power grid reliability. We devise an algorithm that alternates between slow time-scale policy improvement, and fast time-scale value function approximation. We compare our results to prevailing heuristics, and show the strength of our method.
Learning Sparse Combinatorial Representations via Two-stage Submodular Maximization
Authors: Eric Balkanski, Baharan Mirzasoleiman, Andreas Krause, Yaron Singer
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We consider the problem of learning sparse representations of data sets, where the goal is to reduce a data set in manner that optimizes multiple objectives. Motivated by applications of data summarization, we develop a new model which we refer to as the two-stage submodular maximization problem. This task can be viewed as a combinatorial analogue of representation learning problems such as dictionary learning and sparse regression. The two-stage problem strictly generalizes the problem of cardinality constrained submodular maximization, though the objective function is not submodular and the techniques for submodular maximization cannot be applied. We describe a continuous optimization method which achieves an approximation ratio which asymptotically approaches 1-1/e. For instances where the asymptotics do not kick in, we design a local-search algorithm whose approximation ratio is arbitrarily close to 1/2. We empirically demonstrate the effectiveness of our methods on two multi-objective data summarization tasks, where the goal is to construct summaries via sparse representative subsets w.r.t. to predefined objectives.
Understanding and Improving Convolutional Neural Networks via Concatenated Rectified Linear Units
Authors: Wenling Shang, Kihyuk Sohn, Diogo Almeida, Honglak Lee
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Recently, convolutional neural networks (CNNs) have been used as a powerful tool to solve many problems of machine learning and computer vision. In this paper, we aim to provide insight on the property of convolutional neural networks, as well as a generic method to improve the performance of many CNN architectures. Specifically, we first examine existing CNN models and observe an intriguing property that the filters in the lower layers form pairs (i.e., filters with opposite phase). Inspired by our observation, we propose a novel, simple yet effective activation scheme called concatenated ReLU (CReLU) and theoretically analyze its reconstruction property in CNNs. We integrate CReLU into several state-of-the-art CNN architectures and demonstrate improvement in their recognition performance on CIFAR-10/100 and ImageNet datasets with fewer trainable parameters. Our results suggest that better understanding of the properties of CNNs can lead to significant performance improvement with a simple modification.
Isotonic Hawkes Processes
Authors: Yichen Wang, Bo Xie, Nan Du, Le Song
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Hawkes processes are powerful tools for modeling the mutual-excitation phenomena commonly observed in event data from a variety of domains, such as social networks, quantitative finance and healthcare records. The intensity function of a Hawkes process is typically assumed to be linear in the sum of triggering kernels, rendering it inadequate to capture nonlinear effects present in real-world data. To address this shortcoming, we propose an Isotonic-Hawkes process whose intensity function is modulated by an additional nonlinear link function. We also developed a novel iterative algorithm which learns both the nonlinear link function and other parameters provably. We showed that Isotonic-Hawkes processes can fit a variety of nonlinear patterns which cannot be captured by conventional Hawkes processes, and achieve superior empirical performance in real world applications.
Cross-Graph Learning of Multi-Relational Associations
Authors: Hanxiao Liu, Yiming Yang
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Cross-graph Relational Learning (CGRL) refers to the problem of predicting the strengths or labels of multi-relational tuples of heterogeneous object types, through the joint inference over multiple graphs which specify the internal connections among each type of objects. CGRL is an open challenge in machine learning due to the daunting number of all possible tuples to deal with when the numbers of nodes in multiple graphs are large, and because the labeled training instances are extremely sparse as typical. Existing methods such as tensor factorization or tensor-kernel machines do not work well because of the lack of convex formulation for the optimization of CGRL models, the poor scalability of the algorithms in handling combinatorial numbers of tuples, and/or the non-transductive nature of the learning methods which limits their ability to leverage unlabeled data in training. This paper proposes a novel framework which formulates CGRL as a convex optimization problem, enables transductive learning using both labeled and unlabeled tuples, and offers a scalable algorithm that guarantees the optimal solution and enjoys a constant time complexity with respect to the sizes of input graphs. In our experiments with a subset of DBLP publication records and an Enzyme multi-source dataset, the proposed method successfully scaled to the large cross-graph inference problem, and outperformed other representative approaches significantly.
Markov-modulated Marked Poisson Processes for Check-in Data
Authors: Jiangwei Pan, Vinayak Rao, Pankaj Agarwal, Alan Gelfand
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We develop continuous-time probabilistic models to study trajectory data consisting of times and locations of user “check-ins”. We model the data as realizations of a marked point process, with intensity and mark-distribution modulated by a latent Markov jump process (MJP). We also include user-heterogeneity in our model by assigning each user a vector of “preferred locations”. Our model extends latent Dirichlet allocation by dropping the bag-of-words assumption and operating in continuous time. We show how an appropriate choice of priors allows efficient posterior inference. Our experiments demonstrate the usefulness of our approach by comparing with various baselines on a variety of tasks.
Beyond Parity Constraints: Fourier Analysis of Hash Functions for Inference
Authors: Tudor Achim, Ashish Sabharwal, Stefano Ermon
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Random projections have played an important role in scaling up machine learning and data mining algorithms. Recently they have also been applied to probabilistic inference to estimate properties of high-dimensional distributions; however, they all rely on the same class of projections based on universal hashing. We provide a general framework to analyze random projections which relates their statistical properties to their Fourier spectrum, which is a well-studied area of theoretical computer science. Using this framework we introduce two new classes of hash functions for probabilistic inference and model counting that show promising performance on synthetic and real-world benchmarks.
On the Power and Limits of Distance-Based Learning
Authors: Periklis Papakonstantinou, Jia Xu, Guang Yang
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We initiate the study of low-distortion finite metric embeddings in multi-class (and multi-label) classification where (i) both the space of input instances and the space of output classes have combinatorial metric structure and (ii) the concepts we wish to learn are low-distortion embeddings. We develop new geometric techniques and prove strong learning lower bounds. These provable limits hold even when we allow learners and classifiers to get advice by one or more experts. Our study overwhelmingly indicates that post-geometry assumptions are necessary in multi-class classification, as in natural language processing (NLP). Technically, the mathematical tools we developed in this work could be of independent interest to NLP. To the best of our knowledge, this is the first work which formally studies classification problems in combinatorial spaces. and where the concepts are low-distortion embeddings.
A Convex Atomic-Norm Approach to Multiple Sequence Alignment and Motif Discovery
Authors: Ian En-Hsu Yen, Xin Lin, Jiong Zhang, Pradeep Ravikumar, Inderjit Dhillon
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Multiple Sequence Alignment and Motif Discovery, known as NP-hard problems, are two fundamental tasks in Bioinformatics. Existing approaches to these two problems are based on either local search methods such as Expectation Maximization (EM), Gibbs Sampling or greedy heuristic methods. In this work, we develop a convex relaxation approach to both problems based on the recent concept of atomic norm and develop a new algorithm, termed Greedy Direction Method of Multiplier, for solving the convex relaxation with two convex atomic constraints. Experiments show that our convex relaxation approach produces solutions of higher quality than those standard tools widely-used in Bioinformatics community on the Multiple Sequence Alignment and Motif Discovery problems.