mtybilly/Instruct2DS huggingface dataset:
Sequence to Sequence Training of CTC-RNNs with Partial Windowing
Authors: Hwang, Kyuyeon and Sung, Wonyong
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: Mnih, Andriy and Rezende, Danilo
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: Dalal, Gal and Gilboa, Elad and Mannor, Shie
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: Balkanski, Eric and Mirzasoleiman, Baharan and Krause, Andreas and Singer, Yaron
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: Shang, Wenling and Sohn, Kihyuk and Almeida, Diogo and Lee, Honglak
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: Wang, Yichen and Xie, Bo and Du, Nan and Song, Le
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: Liu, Hanxiao and Yang, Yiming
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: Pan, Jiangwei and Rao, Vinayak and Agarwal, Pankaj and Gelfand, Alan
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: Achim, Tudor and Sabharwal, Ashish and Ermon, Stefano
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: Papakonstantinou, Periklis and Xu, Jia and Yang, Guang
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: Yen, Ian En-Hsu and Lin, Xin and Zhang, Jiong and Ravikumar, Pradeep and Dhillon, Inderjit
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.
Generalized Direct Change Estimation in Ising Model Structure
Authors: Fazayeli, Farideh and Banerjee, Arindam
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We consider the problem of estimating change in the dependency structure of two p-dimensional Ising models, based on respectively n_1 and n_2 samples drawn from the models. The change is assumed to be structured, e.g., sparse, block sparse, node-perturbed sparse, etc., such that it can be characterized by a suitable (atomic) norm. We present and analyze a norm-regularized estimator for directly estimating the change in structure, without having to estimate the structures of the individual Ising models. The estimator can work with any norm, and can be generalized to other graphical models under mild assumptions. We show that only one set of samples, say n_2, needs to satisfy the sample complexity requirement for the estimator to work, and the estimation error decreases as \fracc\sqrt\min(n_1,n_2), where c depends on the Gaussian width of the unit norm ball. For example, for \ell_1 norm applied to s-sparse change, the change can be accurately estimated with \min(n_1,n_2)=O(s łog p) which is sharper than an existing result n_1= O(s^2 łog p) and n_2 = O(n_1^2). Experimental results illustrating the effectiveness of the proposed estimator are presented.
Robust Principal Component Analysis with Side Information
Authors: Chiang, Kai-Yang and Hsieh, Cho-Jui and Dhillon, Inderjit
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The robust principal component analysis (robust PCA) problem has been considered in many machine learning applications, where the goal is to decompose the data matrix as a low rank part plus a sparse residual. While current approaches are developed by only considering the low rank plus sparse structure, in many applications, side information of row and/or column entities may also be given, and it is still unclear to what extent could such information help robust PCA. Thus, in this paper, we study the problem of robust PCA with side information, where both prior structure and features of entities are exploited for recovery. We propose a convex problem to incorporate side information in robust PCA and show that the low rank matrix can be exactly recovered via the proposed method under certain conditions. In particular, our guarantee suggests that a substantial amount of low rank matrices, which cannot be recovered by standard robust PCA, become recoverable by our proposed method. The result theoretically justifies the effectiveness of features in robust PCA. In addition, we conduct synthetic experiments as well as a real application on noisy image classification to show that our method also improves the performance in practice by exploiting side information.
Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation
Authors: Gui, Huan and Han, Jiawei and Gu, Quanquan
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present a unified framework for low-rank matrix estimation with a nonconvex penalty. A proximal gradient homotopy algorithm is proposed to solve the proposed optimization problem. Theoretically, we first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain condition on the magnitude of the nonzero singular values, the proposed estimator enjoys oracle property (i.e., exactly recovers the true rank of the matrix), besides attaining a faster rate. Extensive numerical experiments on both synthetic and real world datasets corroborate our theoretical findings.
Early and Reliable Event Detection Using Proximity Space Representation
Authors: Sangnier, Maxime and Gauthier, Jerome and Rakotomamonjy, Alain
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Let us consider a specific action or situation (called event) that takes place within a time series. The objective in early detection is to build a decision function that is able to go off as soon as possible from the onset of an occurrence of this event. This implies making a decision with an incomplete information. This paper proposes a novel framework that i) guarantees that a detection made with a partial observation will also occur at full observation of the time-series; ii) incorporates in a consistent manner the lack of knowledge about the minimal amount of information needed to make a decision. The proposed detector is based on mapping the temporal sequences to a landmarking space thanks to appropriately designed similarity functions. As a by-product, the framework benefits from a scalable training algorithm and a theoretical guarantee concerning its generalization ability. We also discuss an important improvement of our framework in which decision function can still be made reliable while being more expressive. Our experimental studies provide compelling results on toy data, presenting the trade-off that occurs when aiming at accuracy, earliness and reliability. Results on real physiological and video datasets show that our proposed approach is as accurate and early as state-of-the-art algorithm, while ensuring reliability and being far more efficient to learn.
Stratified Sampling Meets Machine Learning
Authors: Liberty, Edo and Lang, Kevin and Shmakov, Konstantin
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: This paper solves a specialized regression problem to obtain sampling probabilities for records in databases. The goal is to sample a small set of records over which evaluating aggregate queries can be done both efficiently and accurately. We provide a principled and provable solution for this problem; it is parameterless and requires no data insights. Unlike standard regression problems, the loss is inversely proportional to the regressed-to values. Moreover, a cost zero solution always exists and can only be excluded by hard budget constraints. A unique form of regularization is also needed. We provide an efficient and simple regularized Empirical Risk Minimization (ERM) algorithm along with a theoretical generalization result. Our extensive experimental results significantly improve over both uniform sampling and standard stratified sampling which are de-facto the industry standards.
Efficient Multi-Instance Learning for Activity Recognition from Time Series Data Using an Auto-Regressive Hidden Markov Model
Authors: Guan, Xinze and Raich, Raviv and Wong, Weng-Keen
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Activity recognition from sensor data has spurred a great deal of interest due to its impact on health care. Prior work on activity recognition from multivariate time series data has mainly applied supervised learning techniques which require a high degree of annotation effort to produce training data with the start and end times of each activity. In order to reduce the annotation effort, we present a weakly supervised approach based on multi-instance learning. We introduce a generative graphical model for multi-instance learning on time series data based on an auto-regressive hidden Markov model. Our model has a number of advantages, including the ability to produce both bag and instance-level predictions as well as an efficient exact inference algorithm based on dynamic programming.
Generalization Properties and Implicit Regularization for Multiple Passes SGM
Authors: Lin, Junhong and Camoriano, Raffaello and Rosasco, Lorenzo
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study the generalization properties of stochastic gradient methods for learning with convex loss functions and linearly parameterized functions. We show that, in the absence of penalizations or constraints, the stability and approximation properties of the algorithm can be controlled by tuning either the step-size or the number of passes over the data. In this view, these parameters can be seen to control a form of implicit regularization. Numerical results complement the theoretical findings.
Principal Component Projection Without Principal Component Analysis
Authors: Frostig, Roy and Musco, Cameron and Musco, Christopher and Sidford, Aaron
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We show how to efficiently project a vector onto the top principal components of a matrix, *without explicitly computing these components*. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependence on the number of top principal components. We show that it can be used to give a fast iterative method for the popular principal component regression problem, giving the first major runtime improvement over the naive method of combining PCA with regression. To achieve our results, we first observe that ridge regression can be used to obtain a "smooth projection" onto the top principal components. We then sharpen this approximation to true projection using a low-degree polynomial approximation to the matrix step function. Step function approximation is a topic of long-term interest in scientific computing. We extend prior theory by constructing polynomials with simple iterative structure and rigorously analyzing their behavior under limited precision.
Recovery guarantee of weighted low-rank approximation via alternating minimization
Authors: Li, Yuanzhi and Liang, Yingyu and Risteski, Andrej
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated as a weighted low-rank approximation problem and solved by non-convex optimization heuristics such as alternating minimization. In this paper, we provide provable recovery guarantee of weighted low-rank via a simple alternating minimization algorithm. In particular, for a natural class of matrices and weights and without any assumption on the noise, we bound the spectral norm of the difference between the recovered matrix and the ground truth, by the spectral norm of the weighted noise plus an additive error term that decreases exponentially with the number of rounds of alternating minimization, from either initialization by SVD or, more importantly, random initialization. These provide the first theoretical results for weighted low-rank approximation via alternating minimization with non-binary deterministic weights, significantly generalizing those for matrix completion, the special case with binary weights, since our assumptions are similar or weaker than those made in existing works. Furthermore, this is achieved by a very simple algorithm that improves the vanilla alternating minimization with a simple clipping step.
Deconstructing the Ladder Network Architecture
Authors: Pezeshki, Mohammad and Fan, Linxi and Brakel, Philemon and Courville, Aaron and Bengio, Yoshua
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The Ladder Network is a recent new approach to semi-supervised learning that turned out to be very successful. While showing impressive performance, the Ladder Network has many components intertwined, whose contributions are not obvious in such a complex architecture. This paper presents an extensive experimental investigation of variants of the Ladder Network in which we replaced or removed individual components to learn about their relative importance. For semi-supervised tasks, we conclude that the most important contribution is made by the lateral connections, followed by the application of noise, and the choice of what we refer to as the ‘combinator function’. As the number of labeled training examples increases, the lateral connections and the reconstruction criterion become less important, with most of the generalization improvement coming from the injection of noise in each layer. Finally, we introduce a combinator function that reduces test error rates on Permutation-Invariant MNIST to 0.57% for the supervised setting, and to 0.97% and 1.0% for semi-supervised settings with 1000 and 100 labeled examples, respectively.
Generalization and Exploration via Randomized Value Functions
Authors: Osband, Ian and Roy, Benjamin Van and Wen, Zheng
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose randomized least-squares value iteration (RLSVI) – a new reinforcement learning algorithm designed to explore and generalize efficiently via linearly parameterized value functions. We explain why versions of least-squares value iteration that use Boltzmann or epsilon-greedy exploration can be highly inefficient, and we present computational results that demonstrate dramatic efficiency gains enjoyed by RLSVI. Further, we establish an upper bound on the expected regret of RLSVI that demonstrates near-optimality in a tabula rasa learning context. More broadly, our results suggest that randomized value functions offer a promising approach to tackling a critical challenge in reinforcement learning: synthesizing efficient exploration and effective generalization.
Evasion and Hardening of Tree Ensemble Classifiers
Authors: Kantchelian, Alex and Tygar, J. D. and Joseph, Anthony
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Classifier evasion consists in finding for a given instance x the “nearest” instance x’ such that the classifier predictions of x and x’ are different. We present two novel algorithms for systematically computing evasions for tree ensembles such as boosted trees and random forests. Our first algorithm uses a Mixed Integer Linear Program solver and finds the optimal evading instance under an expressive set of constraints. Our second algorithm trades off optimality for speed by using symbolic prediction, a novel algorithm for fast finite differences on tree ensembles. On a digit recognition task, we demonstrate that both gradient boosted trees and random forests are extremely susceptible to evasions. Finally, we harden a boosted tree model without loss of predictive accuracy by augmenting the training set of each boosting round with evading instances, a technique we call adversarial boosting.
Dynamic Memory Networks for Visual and Textual Question Answering
Authors: Xiong, Caiming and Merity, Stephen and Socher, Richard
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Neural network architectures with memory and attention mechanisms exhibit certain reason- ing capabilities required for question answering. One such architecture, the dynamic memory net- work (DMN), obtained high accuracy on a variety of language tasks. However, it was not shown whether the architecture achieves strong results for question answering when supporting facts are not marked during training or whether it could be applied to other modalities such as images. Based on an analysis of the DMN, we propose several improvements to its memory and input modules. Together with these changes we introduce a novel input module for images in order to be able to answer visual questions. Our new DMN+ model improves the state of the art on both the Visual Question Answering dataset and the bAbI-10k text question-answering dataset without supporting fact supervision.
Estimating Cosmological Parameters from the Dark Matter Distribution
Authors: Ravanbakhsh, Siamak and Oliva, Junier and Fromenteau, Sebastian and Price, Layne and Ho, Shirley and Schneider, Jeff and Poczos, Barnabas
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach in estimating the cosmological parameters is to use the large scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in three dimensions. Information about galaxy locations is typically summarized in a "single" function of scale, such as the galaxy correlation function or power-spectrum. We show that it is possible to estimate these cosmological parameters directly from the distribution of matter. This paper presents the application of deep 3D convolutional networks to volumetric representation of dark matter simulations as well as the results obtained using a recently proposed distribution regression framework, showing that machine learning techniques are comparable to, and can sometimes outperform, maximum-likelihood point estimates using "cosmological models". This opens the way to estimating the parameters of our Universe with higher accuracy.
Learning Population-Level Diffusions with Generative RNNs
Authors: Hashimoto, Tatsunori and Gifford, David and Jaakkola, Tommi
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We estimate stochastic processes that govern the dynamics of evolving populations such as cell differentiation. The problem is challenging since longitudinal trajectory measurements of individuals in a population are rarely available due to experimental cost and/or privacy. We show that cross-sectional samples from an evolving population suffice for recovery within a class of processes even if samples are available only at a few distinct time points. We provide a stratified analysis of recoverability conditions, and establish that reversibility is sufficient for recoverability. For estimation, we derive a natural loss and regularization, and parameterize the processes as diffusive recurrent neural networks. We demonstrate the approach in the context of uncovering complex cellular dynamics known as the ‘epigenetic landscape’ from existing biological assays.
Expressiveness of Rectifier Networks
Authors: Pan, Xingyuan and Srikumar, Vivek
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Rectified Linear Units (ReLUs) have been shown to ameliorate the vanishing gradient problem, allow for efficient backpropagation, and empirically promote sparsity in the learned parameters. They have led to state-of-the-art results in a variety of applications. However, unlike threshold and sigmoid networks, ReLU networks are less explored from the perspective of their expressiveness. This paper studies the expressiveness of ReLU networks. We characterize the decision boundary of two-layer ReLU networks by constructing functionally equivalent threshold networks. We show that while the decision boundary of a two-layer ReLU network can be captured by a threshold network, the latter may require an exponentially larger number of hidden units. We also formulate sufficient conditions for a corresponding logarithmic reduction in the number of hidden units to represent a sign network as a ReLU network. Finally, we experimentally compare threshold networks and their much smaller ReLU counterparts with respect to their ability to learn from synthetically generated data.
Discrete Distribution Estimation under Local Privacy
Authors: Kairouz, Peter and Bonawitz, Keith and Ramage, Daniel
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The collection and analysis of user data drives improvements in the app and web ecosystems, but comes with risks to privacy. This paper examines discrete distribution estimation under local privacy, a setting wherein service providers can learn the distribution of a categorical statistic of interest without collecting the underlying data. We present new mechanisms, including hashed k-ary Randomized Response (KRR), that empirically meet or exceed the utility of existing mechanisms at all privacy levels. New theoretical results demonstrate the order-optimality of KRR and the existing RAPPOR mechanism at different privacy regimes.
Square Root Graphical Models: Multivariate Generalizations of Univariate Exponential Families that Permit Positive Dependencies
Authors: Inouye, David and Ravikumar, Pradeep and Dhillon, Inderjit
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models [Yang et al. 2015] did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York—modeled as an exponential distribution—is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix—a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with \ell_1 regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times.
A Box-Constrained Approach for Hard Permutation Problems
Authors: Lim, Cong Han and Wright, Steve
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We describe the use of sorting networks to form relaxations of problems involving permutations of n objects. This approach is an alternative to relaxations based on the Birkhoff polytope (the set of n \times n doubly stochastic matrices), providing a more compact formulation in which the only constraints are box constraints. Using this approach, we form a variant of the relaxation of the quadratic assignment problem recently studied in Vogelstein et al. (2015), and show that the continuation method applied to this formulation can be quite effective. We develop a coordinate descent algorithm that achieves a per-cycle complexity of O(n^2 łog^2 n). We compare this method with Fast Approximate QAP (FAQ) algorithm introduced in Vogelstein et al. (2015), which uses a conditional-gradient method whose per-iteration complexity is O(n^3). We demonstrate that for most problems in QAPLIB and for a class of synthetic QAP problems, the sorting-network formulation returns solutions that are competitive with the FAQ algorithm, often in significantly less computing time.
Geometric Mean Metric Learning
Authors: Zadeh, Pourya and Hosseini, Reshad and Sra, Suvrit
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric appeal through the Riemannian geometry of positive definite matrices; (ii) ease of interpretability; and (iii) computational speed several orders of magnitude faster than the widely used LMNN and ITML methods. Furthermore, on standard benchmark datasets, our closed-form solution consistently attains higher classification accuracy.
Sparse Nonlinear Regression: Parameter Estimation under Nonconvexity
Authors: Yang, Zhuoran and Wang, Zhaoran and Liu, Han and Eldar, Yonina and Zhang, Tong
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study parameter estimation for sparse nonlinear regression. More specifically, we assume the data are given by y = f( \bf x^T \bf β^* ) + ε, where f is nonlinear. To recover \bf βs, we propose an \ell_1-regularized least-squares estimator. Unlike classical linear regression, the corresponding optimization problem is nonconvex because of the nonlinearity of f. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. Detailed numerical results are provided to back up our theory.
Conditional Bernoulli Mixtures for Multi-label Classification
Authors: Li, Cheng and Wang, Bingyu and Pavlu, Virgil and Aslam, Javed
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Multi-label classification is an important machine learning task wherein one assigns a subset of candidate labels to an object. In this paper, we propose a new multi-label classification method based on Conditional Bernoulli Mixtures. Our proposed method has several attractive properties: it captures label dependencies; it reduces the multi-label problem to several standard binary and multi-class problems; it subsumes the classic independent binary prediction and power-set subset prediction methods as special cases; and it exhibits accuracy and/or computational complexity advantages over existing approaches. We demonstrate two implementations of our method using logistic regressions and gradient boosted trees, together with a simple training procedure based on Expectation Maximization. We further derive an efficient prediction procedure based on dynamic programming, thus avoiding the cost of examining an exponential number of potential label subsets. Experimental results show the effectiveness of the proposed method against competitive alternatives on benchmark datasets.
Scalable Discrete Sampling as a Multi-Armed Bandit Problem
Authors: Chen, Yutian and Ghahramani, Zoubin
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We study the problem of sampling a discrete random variable with a high degree of dependency that is typical in large-scale Bayesian inference and graphical models, and propose an efficient approximate solution with a subsampling approach. We make a novel connection between the discrete sampling and Multi-Armed Bandits problems with a finite reward population and provide three algorithms with theoretical guarantees. Empirical evaluations show the robustness and efficiency of the approximate algorithms in both synthetic and real-world large-scale problems.
Recycling Randomness with Structure for Sublinear time Kernel Expansions
Authors: Choromanski, Krzysztof and Sindhwani, Vikas
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose a scheme for recycling Gaussian random vectors into structured matrices to ap- proximate various kernel functions in sublin- ear time via random embeddings. Our frame- work includes the Fastfood construction of Le et al. (2013) as a special case, but also ex- tends to Circulant, Toeplitz and Hankel matri- ces, and the broader family of structured matri- ces that are characterized by the concept of low- displacement rank. We introduce notions of co- herence and graph-theoretic structural constants that control the approximation quality, and prove unbiasedness and low-variance properties of ran- dom feature maps that arise within our frame- work. For the case of low-displacement matri- ces, we show how the degree of structure and randomness can be controlled to reduce statis- tical variance at the cost of increased computa- tion and storage requirements. Empirical results strongly support our theory and justify the use of a broader family of structured matrices for scal- ing up kernel methods using random features.
Bidirectional Helmholtz Machines
Authors: Bornschein, Jorg and Shabanian, Samira and Fischer, Asja and Bengio, Yoshua
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine or Variational Autoencoder, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better generative models can be obtained with better approximate inference procedures. Instead of improving the inference procedure, we here propose a new model, the bidirectional Helmholtz machine, which guarantees that the top-down and bottom-up distributions can efficiently invert each other. We achieve this by interpreting both the top-down and the bottom-up directed models as approximate inference distributions and by defining the model distribution to be the geometric mean of these two. We present a lower-bound for the likelihood of this model and we show that optimizing this bound regularizes the model so that the Bhattacharyya distance between the bottom-up and top-down approximate distributions is minimized. This approach results in state of the art generative models which prefer significantly deeper architectures while it allows for orders of magnitude more efficient likelihood estimation.
Faster Convex Optimization: Simulated Annealing with an Efficient Universal Barrier
Authors: Abernethy, Jacob and Hazan, Elad
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: This paper explores a surprising equivalence between two seemingly-distinct convex optimization methods. We show that simulated annealing, a well-studied random walk algorithms, is *directly equivalent*, in a certain sense, to the central path interior point algorithm for the the entropic universal barrier function. This connection exhibits several benefits. First, we are able improve the state of the art time complexity for convex optimization under the membership oracle model by devising a new temperature schedule for simulated annealing motivated by central path following interior point methods. Second, we get an efficient randomized interior point method with an efficiently computable universal barrier for any convex set described by a membership oracle. Previously, efficiently computable barriers were known only for particular convex sets.
Preconditioning Kernel Matrices
Authors: Cutajar, Kurt and Osborne, Michael and Cunningham, John and Filippone, Maurizio
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves the constraints on both storage (the kernel matrix need not be stored) and computation (both stochastic gradients and parallelization can be used). Even so, conjugate gradient is not without its own issues: the conditioning of kernel matrices is often such that conjugate gradients will have poor convergence in practice. Preconditioning is a common approach to alleviating this issue. Here we propose preconditioned conjugate gradients for kernel machines, and develop a broad range of preconditioners particularly useful for kernel matrices. We describe a scalable approach to both solving kernel machines and learning their hyperparameters. We show this approach is exact in the limit of iterations and outperforms state-of-the-art approximations for a given computational budget.
Greedy Column Subset Selection: New Bounds and Distributed Algorithms
Authors: Altschuler, Jason and Bhaskara, Aditya and Fu, Gang and Mirrokni, Vahab and Rostamizadeh, Afshin and Zadimoghaddam, Morteza
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy algorithm has been shown to be quite effective in practice. However, theoretical guarantees on its performance have not been explored thoroughly, especially in a distributed setting. In this paper, we study the greedy algorithm for the column subset selection problem from a theoretical and empirical perspective and show its effectiveness in a distributed setting. In particular, we provide an improved approximation guarantee for the greedy algorithm which we show is tight up to a constant factor, and present the first distributed implementation with provable approximation factors. We use the idea of randomized composable core-sets, developed recently in the context of submodular maximization. Finally, we validate the effectiveness of this distributed algorithm via an empirical study.