mtybilly/Instruct2DS huggingface dataset:
spred: Solving L1 Penalty with SGD
Authors: Liu Ziyin, Zihao Wang
Published in: Proceedings of the 40th International Conference on Machine Learning (Main Conference Track), 2023

Abstract: We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, spred, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely “benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.
The Benefits of Mixup for Feature Learning
Authors: Difan Zou, Yuan Cao, Yuanzhi Li, Quanquan Gu
Published in: Proceedings of the 40th International Conference on Machine Learning (Main Conference Track), 2023

Abstract: Mixup, a simple data augmentation method that randomly mixes two data points via linear interpolation, has been extensively applied in various deep learning applications to gain better generalization. However, its theoretical explanation remains largely unclear. In this work, we aim to seek a fundamental understanding of the benefits of Mixup. We first show that Mixup using different linear interpolation parameters for features and labels can still achieve similar performance as standard Mixup. This indicates that the intuitive linearity explanation in Zhang et al., (2018) may not fully explain the success of Mixup. Then, we perform a theoretical study of Mixup from the feature learning perspective. We consider a feature-noise data model and show that Mixup training can effectively learn the rare features (appearing in a small fraction of data) from its mixture with the common features (appearing in a large fraction of data). In contrast, standard training can only learn the common features but fails to learn the rare features, thus suffering from bad generalization performance. Moreover, our theoretical analysis also shows that the benefits of Mixup for feature learning are mostly gained in the early training phase, based on which we propose to apply early stopping in Mixup. Experimental results verify our theoretical findings and demonstrate the effectiveness of the early-stopped Mixup training.
No Oops, You Won't Do It Again: Mechanisms for Self-correction in Crowdsourcing
Authors: Nihar Shah, Dengyong Zhou
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Crowdsourcing is a very popular means of obtaining the large amounts of labeled data that modern machine learning methods require. Although cheap and fast to obtain, crowdsourced labels suffer from significant amounts of error, thereby degrading the performance of downstream machine learning tasks. With the goal of improving the quality of the labeled data, we seek to mitigate the many errors that occur due to silly mistakes or inadvertent errors by crowdsourcing workers. We propose a two-stage setting for crowdsourcing where the worker first answers the questions, and is then allowed to change her answers after looking at a (noisy) reference answer. We mathematically formulate this process and develop mechanisms to incentivize workers to act appropriately. Our mathematical guarantees show that our mechanism incentivizes the workers to answer honestly in both stages, and refrain from answering randomly in the first stage or simply copying in the second. Numerical experiments reveal a significant boost in performance that such "self-correction" can provide when using crowdsourcing to train machine learning algorithms.
Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues
Authors: Nihar Shah, Sivaraman Balakrishnan, Aditya Guntuboyina, Martin Wainwright
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are required only to satisfy a natural form of stochastic transitivity. This class includes parametric models including the BTL and Thurstone models as special cases, but is considerably more general. We provide various examples of models in this broader stochastically transitive class for which classical parametric models provide poor fits. Despite this greater flexibility, we show that the matrix of probabilities can be estimated at the same rate as in standard parametric models. On the other hand, unlike in the BTL and Thurstone models, computing the minimax-optimal estimator in the stochastically transitive model is non-trivial, and we explore various computationally tractable alternatives. We show that a simple singular value thresholding algorithm is statistically consistent but does not achieve the minimax rate. We then propose and study algorithms that achieve the minimax rate over interesting sub-classes of the full stochastically transitive class. We complement our theoretical results with thorough numerical simulations.
Uprooting and Rerooting Graphical Models
Authors: Adrian Weller
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We show how any binary pairwise model may be “uprooted” to a fully symmetric model, wherein original singleton potentials are transformed to potentials on edges to an added variable, and then “rerooted” to a new model on the original number of variables. The new model is essentially equivalent to the original model, with the same partition function and allowing recovery of the original marginals or a MAP configuration, yet may have very different computational properties that allow much more efficient inference. This meta-approach deepens our understanding, may be applied to any existing algorithm to yield improved methods in practice, generalizes earlier theoretical results, and reveals a remarkable interpretation of the triplet-consistent polytope.
A Deep Learning Approach to Unsupervised Ensemble Learning
Authors: Uri Shaham, Xiuyuan Cheng, Omer Dror, Ariel Jaffe, Boaz Nadler, Joseph Chang, Yuval Kluger
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We show how deep learning methods can be applied in the context of crowdsourcing and unsupervised ensemble learning. First, we prove that the popular model of Dawid and Skene, which assumes that all classifiers are conditionally independent, is \em equivalent to a Restricted Boltzmann Machine (RBM) with a single hidden node. Hence, under this model, the posterior probabilities of the true labels can be instead estimated via a trained RBM. Next, to address the more general case, where classifiers may strongly violate the conditional independence assumption, we propose to apply RBM-based Deep Neural Net (DNN). Experimental results on various simulated and real-world datasets demonstrate that our proposed DNN approach outperforms other state-of-the-art methods, in particular when the data violates the conditional independence assumption.
Revisiting Semi-Supervised Learning with Graph Embeddings
Authors: Zhilin Yang, William Cohen, Ruslan Salakhudinov
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present a semi-supervised learning framework based on graph embeddings. Given a graph between instances, we train an embedding for each instance to jointly predict the class label and the neighborhood context in the graph. We develop both transductive and inductive variants of our method. In the transductive variant of our method, the class labels are determined by both the learned embeddings and input feature vectors, while in the inductive variant, the embeddings are defined as a parametric function of the feature vectors, so predictions can be made on instances not seen during training. On a large and diverse set of benchmark tasks, including text classification, distantly supervised entity extraction, and entity classification, we show improved performance over many of the existing models.
Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimization
Authors: Chelsea Finn, Sergey Levine, Pieter Abbeel
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Reinforcement learning can acquire complex behaviors from high-level specifications. However, defining a cost function that can be optimized effectively and encodes the correct task is challenging in practice. We explore how inverse optimal control (IOC) can be used to learn behaviors from demonstrations, with applications to torque control of high-dimensional robotic systems. Our method addresses two key challenges in inverse optimal control: first, the need for informative features and effective regularization to impose structure on the cost, and second, the difficulty of learning the cost function under unknown dynamics for high-dimensional continuous systems. To address the former challenge, we present an algorithm capable of learning arbitrary nonlinear cost functions, such as neural networks, without meticulous feature engineering. To address the latter challenge, we formulate an efficient sample-based approximation for MaxEnt IOC. We evaluate our method on a series of simulated tasks and real-world robotic manipulation problems, demonstrating substantial improvement over prior methods both in terms of task complexity and sample efficiency.
Diversity-Promoting Bayesian Learning of Latent Variable Models
Authors: Pengtao Xie, Jun Zhu, Eric Xing
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In learning latent variable models (LVMs), it is important to effectively capture infrequent patterns and shrink model size without sacrificing modeling power. Various studies have been done to “diversify” a LVM, which aim to learn a diverse set of latent components in LVMs. Most existing studies fall into a frequentist-style regularization framework, where the components are learned via point estimation. In this paper, we investigate how to “diversify” LVMs in the paradigm of Bayesian learning, which has advantages complementary to point estimation, such as alleviating overfitting via model averaging and quantifying uncertainty. We propose two approaches that have complementary advantages. One is to define diversity-promoting mutual angular priors which assign larger density to components with larger mutual angles based on Bayesian network and von Mises-Fisher distribution and use these priors to affect the posterior via Bayes rule. We develop two efficient approximate posterior inference algorithms based on variational inference and Markov chain Monte Carlo sampling. The other approach is to impose diversity-promoting regularization directly over the post-data distribution of components. These two methods are applied to the Bayesian mixture of experts model to encourage the “experts” to be diverse and experimental results demonstrate the effectiveness and efficiency of our methods.
Additive Approximations in High Dimensional Nonparametric Regression via the SALSA
Authors: Kirthevasan Kandasamy, Yaoliang Yu
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: High dimensional nonparametric regression is an inherently difficult problem with known lower bounds depending exponentially in dimension. A popular strategy to alleviate this curse of dimensionality has been to use additive models of \emphfirst order, which model the regression function as a sum of independent functions on each dimension. Though useful in controlling the variance of the estimate, such models are often too restrictive in practical settings. Between non-additive models which often have large variance and first order additive models which have large bias, there has been little work to exploit the trade-off in the middle via additive models of intermediate order. In this work, we propose salsa, which bridges this gap by allowing interactions between variables, but controls model capacity by limiting the order of interactions. salsas minimises the residual sum of squares with squared RKHS norm penalties. Algorithmically, it can be viewed as Kernel Ridge Regression with an additive kernel. When the regression function is additive, the excess risk is only polynomial in dimension. Using the Girard-Newton formulae, we efficiently sum over a combinatorial number of terms in the additive expansion. Via a comparison on 15 real datasets, we show that our method is competitive against 21 other alternatives.
Hawkes Processes with Stochastic Excitations
Authors: Young Lee, Kar Wai Lim, Cheng Soon Ong
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.
Data-driven Rank Breaking for Efficient Rank Aggregation
Authors: Ashish Khetan, Sewoong Oh
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. To reduce the computational complexity of learning the global ranking, a common practice is to use rank-breaking. Individuals’ preferences are broken into pairwise comparisons and then applied to efficient algorithms tailored for independent pairwise comparisons. However, due to the ignored dependencies, naive rank-breaking approaches can result in inconsistent estimates. The key idea to produce unbiased and accurate estimates is to treat the paired comparisons outcomes unequally, depending on the topology of the collected data. In this paper, we provide the optimal rank-breaking estimator, which not only achieves consistency but also achieves the best error bound. This allows us to characterize the fundamental tradeoff between accuracy and complexity in some canonical scenarios. Further, we identify how the accuracy depends on the spectral gap of a corresponding comparison graph.
Dropout distillation
Authors: Samuel Rota Bulò, Lorenzo Porzi, Peter Kontschieder
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Dropout is a popular stochastic regularization technique for deep neural networks that works by randomly dropping (i.e. zeroing) units from the network during training. This randomization process allows to implicitly train an ensemble of exponentially many networks sharing the same parametrization, which should be averaged at test time to deliver the final prediction. A typical workaround for this intractable averaging operation consists in scaling the layers undergoing dropout randomization. This simple rule called ’standard dropout’ is efficient, but might degrade the accuracy of the prediction. In this work we introduce a novel approach, coined ’dropout distillation’, that allows us to train a predictor in a way to better approximate the intractable, but preferable, averaging process, while keeping under control its computational efficiency. We are thus able to construct models that are as efficient as standard dropout, or even more efficient, while being more accurate. Experiments on standard benchmark datasets demonstrate the validity of our method, yielding consistent improvements over conventional dropout.
Metadata-conscious anonymous messaging
Authors: Giulia Fanti, Peter Kairouz, Sewoong Oh, Kannan Ramchandran, Pramod Viswanath
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Anonymous messaging platforms like Whisper and Yik Yak allow users to spread messages over a network (e.g., a social network) without revealing message authorship to other users. The spread of messages on these platforms can be modeled by a diffusion process over a graph. Recent advances in network analysis have revealed that such diffusion processes are vulnerable to author deanonymization by adversaries with access to metadata, such as timing information. In this work, we ask the fundamental question of how to propagate anonymous messages over a graph to make it difficult for adversaries to infer the source. In particular, we study the performance of a message propagation protocol called adaptive diffusion introduced in (Fanti et al., 2015). We prove that when the adversary has access to metadata at a fraction of corrupted graph nodes, adaptive diffusion achieves asymptotically optimal source-hiding and significantly outperforms standard diffusion. We further demonstrate empirically that adaptive diffusion hides the source effectively on real social networks.
The Teaching Dimension of Linear Learners
Authors: Ji Liu, Xiaojin Zhu, Hrag Ohannessian
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Teaching dimension is a learning theoretic quantity that specifies the minimum training set size to teach a target model to a learner. Previous studies on teaching dimension focused on version-space learners which maintain all hypotheses consistent with the training data, and cannot be applied to modern machine learners which select a specific hypothesis via optimization. This paper presents the first known teaching dimension for ridge regression, support vector machines, and logistic regression. We also exhibit optimal training sets that match these teaching dimensions. Our approach generalizes to other linear learners.
Truthful Univariate Estimators
Authors: Ioannis Caragiannis, Ariel Procaccia, Nisarg Shah
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We revisit the classic problem of estimating the population mean of an unknown single-dimensional distribution from samples, taking a game-theoretic viewpoint. In our setting, samples are supplied by strategic agents, who wish to pull the estimate as close as possible to their own value. In this setting, the sample mean gives rise to manipulation opportunities, whereas the sample median does not. Our key question is whether the sample median is the best (in terms of mean squared error) truthful estimator of the population mean. We show that when the underlying distribution is symmetric, there are truthful estimators that dominate the median. Our main result is a characterization of worst-case optimal truthful estimators, which provably outperform the median, for possibly asymmetric distributions with bounded support.
Why Regularized Auto-Encoders learn Sparse Representation?
Authors: Devansh Arpit, Yingbo Zhou, Hung Ngo, Venu Govindaraju
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Sparse distributed representation is the key to learning useful features in deep learning algorithms, because not only it is an efficient mode of data representation, but also – more importantly – it captures the generation process of most real world data. While a number of regularized auto-encoders (AE) enforce sparsity explicitly in their learned representation and others don’t, there has been little formal analysis on what encourages sparsity in these models in general. Our objective is to formally study this general problem for regularized auto-encoders. We provide sufficient conditions on both regularization and activation functions that encourage sparsity. We show that multiple popular models (de-noising and contractive auto encoders, e.g.) and activations (rectified linear and sigmoid, e.g.) satisfy these conditions; thus, our conditions help explain sparsity in their learned representation. Thus our theoretical and empirical analysis together shed light on the properties of regularization/activation that are conductive to sparsity and unify a number of existing auto-encoder models and activation functions under the same analytical framework.
k-variates++: more pluses in the k-means++
Authors: Richard Nock, Raphael Canyasse, Roksana Boreli, Frank Nielsen
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: k-means++ seeding has become a de facto standard for hard clustering algorithms. In this paper, our first contribution is a two-way generalisation of this seeding, k-variates++, that includes the sampling of general densities rather than just a discrete set of Dirac densities anchored at the point locations, *and* a generalisation of the well known Arthur-Vassilvitskii (AV) approximation guarantee, in the form of a *bias+variance* approximation bound of the *global* optimum. This approximation exhibits a reduced dependency on the "noise" component with respect to the optimal potential — actually approaching the statistical lower bound. We show that k-variates++ *reduces* to efficient (biased seeding) clustering algorithms tailored to specific frameworks; these include distributed, streaming and on-line clustering, with *direct* approximation results for these algorithms. Finally, we present a novel application of k-variates++ to differential privacy. For either the specific frameworks considered here, or for the differential privacy setting, there is little to no prior results on the direct application of k-means++ and its approximation bounds — state of the art contenders appear to be significantly more complex and / or display less favorable (approximation) properties. We stress that our algorithms can still be run in cases where there is *no* closed form solution for the population minimizer. We demonstrate the applicability of our analysis via experimental evaluation on several domains and settings, displaying competitive performances vs state of the art.
Multi-Player Bandits -- a Musical Chairs Approach
Authors: Jonathan Rosenski, Ohad Shamir, Liran Szlak
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We consider a variant of the stochastic multi-armed bandit problem, where multiple players simultaneously choose from the same set of arms and may collide, receiving no reward. This setting has been motivated by problems arising in cognitive radio networks, and is especially challenging under the realistic assumption that communication between players is limited. We provide a communication-free algorithm (Musical Chairs) which attains constant regret with high probability, as well as a sublinear-regret, communication-free algorithm (Dynamic Musical Chairs) for the more difficult setting of players dynamically entering and leaving throughout the game. Moreover, both algorithms do not require prior knowledge of the number of players. To the best of our knowledge, these are the first communication-free algorithms with these types of formal guarantees.
The Information Sieve
Authors: Greg Ver Steeg, Aram Galstyan
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We introduce a new framework for unsupervised learning of representations based on a novel hierarchical decomposition of information. Intuitively, data is passed through a series of progressively fine-grained sieves. Each layer of the sieve recovers a single latent factor that is maximally informative about multivariate dependence in the data. The data is transformed after each pass so that the remaining unexplained information trickles down to the next layer. Ultimately, we are left with a set of latent factors explaining all the dependence in the original data and remainder information consisting of independent noise. We present a practical implementation of this framework for discrete variables and apply it to a variety of fundamental tasks in unsupervised learning including independent component analysis, lossy and lossless compression, and predicting missing values in data.
Deep Speech 2 : End-to-End Speech Recognition in English and Mandarin
Authors: Dario Amodei, Sundaram Ananthanarayanan, Rishita Anubhai, Jingliang Bai, Eric Battenberg, Carl Case, Jared Casper, Bryan Catanzaro, Qiang Cheng, Guoliang Chen, Jie Chen, Jingdong Chen, Zhijie Chen, Mike Chrzanowski, Adam Coates, Greg Diamos, Ke Ding, Niandong Du, Erich Elsen, Jesse Engel, Weiwei Fang, Linxi Fan, Christopher Fougner, Liang Gao, Caixia Gong, Awni Hannun, Tony Han, Lappi Johannes, Bing Jiang, Cai Ju, Billy Jun, Patrick LeGresley, Libby Lin, Junjie Liu, Yang Liu, Weigao Li, Xiangang Li, Dongpeng Ma, Sharan Narang, Andrew Ng, Sherjil Ozair, Yiping Peng, Ryan Prenger, Sheng Qian, Zongfeng Quan, Jonathan Raiman, Vinay Rao, Sanjeev Satheesh, David Seetapun, Shubho Sengupta, Kavya Srinet, Anuroop Sriram, Haiyuan Tang, Liliang Tang, Chong Wang, Jidong Wang, Kaifu Wang, Yi Wang, Zhijian Wang, Zhiqian Wang, Shuang Wu, Likai Wei, Bo Xiao, Wen Xie, Yan Xie, Dani Yogatama, Bin Yuan, Jun Zhan, Zhenyao Zhu
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We show that an end-to-end deep learning approach can be used to recognize either English or Mandarin Chinese speech–two vastly different languages. Because it replaces entire pipelines of hand-engineered components with neural networks, end-to-end learning allows us to handle a diverse variety of speech including noisy environments, accents and different languages. Key to our approach is our application of HPC techniques, enabling experiments that previously took weeks to now run in days. This allows us to iterate more quickly to identify superior architectures and algorithms. As a result, in several cases, our system is competitive with the transcription of human workers when benchmarked on standard datasets. Finally, using a technique called Batch Dispatch with GPUs in the data center, we show that our system can be inexpensively deployed in an online setting, delivering low latency when serving users at scale.
On the Consistency of Feature Selection With Lasso for Non-linear Targets
Authors: Yue Zhang, Weihong Guo, Soumya Ray
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: An important question in feature selection is whether a selection strategy recovers the “true” set of features, given enough data. We study this question in the context of the popular Least Absolute Shrinkage and Selection Operator (Lasso) feature selection strategy. In particular, we consider the scenario when the model is misspecified so that the learned model is linear while the underlying real target is nonlinear. Surprisingly, we prove that under certain conditions, Lasso is still able to recover the correct features in this case. We also carry out numerical studies to empirically verify the theoretical results and explore the necessity of the conditions under which the proof holds.
Minimum Regret Search for Single- and Multi-Task Optimization
Authors: Jan Hendrik Metzen
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose minimum regret search (MRS), a novel acquisition function for Bayesian optimization. MRS bears similarities with information-theoretic approaches such as entropy search (ES). However, while ES aims in each query at maximizing the information gain with respect to the global maximum, MRS aims at minimizing the expected simple regret of its ultimate recommendation for the optimum. While empirically ES and MRS perform similar in most of the cases, MRS produces fewer outliers with high simple regret than ES. We provide empirical results both for a synthetic single-task optimization problem as well as for a simulated multi-task robotic control problem.
CryptoNets: Applying Neural Networks to Encrypted Data with High Throughput and Accuracy
Authors: Ran Gilad-Bachrach, Nathan Dowlin, Kim Laine, Kristin Lauter, Michael Naehrig, John Wernsing
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Applying machine learning to a problem which involves medical, financial, or other types of sensitive data, not only requires accurate predictions but also careful attention to maintaining data privacy and security. Legal and ethical requirements may prevent the use of cloud-based machine learning solutions for such tasks. In this work, we will present a method to convert learned neural networks to CryptoNets, neural networks that can be applied to encrypted data. This allows a data owner to send their data in an encrypted form to a cloud service that hosts the network. The encryption ensures that the data remains confidential since the cloud does not have access to the keys needed to decrypt it. Nevertheless, we will show that the cloud service is capable of applying the neural network to the encrypted data to make encrypted predictions, and also return them in encrypted form. These encrypted predictions can be sent back to the owner of the secret key who can decrypt them. Therefore, the cloud service does not gain any information about the raw data nor about the prediction it made. We demonstrate CryptoNets on the MNIST optical character recognition tasks. CryptoNets achieve 99% accuracy and can make around 59000 predictions per hour on a single PC. Therefore, they allow high throughput, accurate, and private predictions.
The Variational Nystrom method for large-scale spectral problems
Authors: Max Vladymyrov, Miguel Carreira-Perpinan
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Spectral methods for dimensionality reduction and clustering require solving an eigenproblem defined by a sparse affinity matrix. When this matrix is large, one seeks an approximate solution. The standard way to do this is the Nystrom method, which first solves a small eigenproblem considering only a subset of landmark points, and then applies an out-of-sample formula to extrapolate the solution to the entire dataset. We show that by constraining the original problem to satisfy the Nystrom formula, we obtain an approximation that is computationally simple and efficient, but achieves a lower approximation error using fewer landmarks and less runtime. We also study the role of normalization in the computational cost and quality of the resulting solution.
Multi-Bias Non-linear Activation in Deep Neural Networks
Authors: Hongyang Li, Wanli Ouyang, Xiaogang Wang
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: As a widely used non-linear activation, Rectified Linear Unit (ReLU) separates noise and signal in a feature map by learning a threshold or bias. However, we argue that the classification of noise and signal not only depends on the magnitude of responses, but also the context of how the feature responses would be used to detect more abstract patterns in higher layers. In order to output multiple response maps with magnitude in different ranges for a particular visual pattern, existing networks employing ReLU and its variants have to learn a large number of redundant filters. In this paper, we propose a multi-bias non-linear activation (MBA) layer to explore the information hidden in the magnitudes of responses. It is placed after the convolution layer to decouple the responses to a convolution kernel into multiple maps by multi-thresholding magnitudes, thus generating more patterns in the feature space at a low computational cost. It provides great flexibility of selecting responses to different visual patterns in different magnitude ranges to form rich representations in higher layers. Such a simple and yet effective scheme achieves the state-of-the-art performance on several benchmarks.
Asymmetric Multi-task Learning Based on Task Relatedness and Loss
Authors: Giwoong Lee, Eunho Yang, Sung Hwang
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose a novel multi-task learning method that can minimize the effect of negative transfer by allowing asymmetric transfer between the tasks based on task relatedness as well as the amount of individual task losses, which we refer to as Asymmetric Multi-task Learning (AMTL). To tackle this problem, we couple multiple tasks via a sparse, directed regularization graph, that enforces each task parameter to be reconstructed as a sparse combination of other tasks, which are selected based on the task-wise loss. We present two different algorithms to solve this joint learning of the task predictors and the regularization graph. The first algorithm solves for the original learning objective using alternative optimization, and the second algorithm solves an approximation of it using curriculum learning strategy, that learns one task at a time. We perform experiments on multiple datasets for classification and regression, on which we obtain significant improvements in performance over the single task learning and symmetric multitask learning baselines.
Accurate Robust and Efficient Error Estimation for Decision Trees
Authors: Lixin Fan
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: This paper illustrates a novel approach to the estimation of generalization error of decision tree classifiers. We set out the study of decision tree errors in the context of consistency analysis theory, which proved that the Bayes error can be achieved only if when the number of data samples thrown into each leaf node goes to infinity. For the more challenging and practical case where the sample size is finite or small, a novel sampling error term is introduced in this paper to cope with the small sample problem effectively and efficiently. Extensive experimental results show that the proposed error estimate is superior to the well known K-fold cross validation methods in terms of robustness and accuracy. Moreover it is orders of magnitudes more efficient than cross validation methods.
Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity
Authors: Ohad Shamir
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study the convergence properties of the VR-PCA algorithm introduced by (Shamir, 2015) for fast computation of leading singular vectors. We prove several new results, including a formal analysis of a block version of the algorithm, and convergence from random initialization. We also make a few observations of independent interest, such as how pre-initializing with just a single exact power iteration can significantly improve the analysis, and what are the convexity and non-convexity properties of the underlying optimization problem.
Convergence of Stochastic Gradient Descent for PCA
Authors: Ohad Shamir
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in R^d. A simple and computationally cheap algorithm for this is stochastic gradient descent (SGD), which incrementally updates its estimate based on each new data point. However, due to the non-convex nature of the problem, analyzing its performance has been a challenge. In particular, existing guarantees rely on a non-trivial eigengap assumption on the covariance matrix, which is intuitively unnecessary. In this paper, we provide (to the best of our knowledge) the first eigengap-free convergence guarantees for SGD in the context of PCA. This also partially resolves an open problem posed in (Hardt & Price, 2014). Moreover, under an eigengap assumption, we show that the same techniques lead to new SGD convergence guarantees with better dependence on the eigengap.
Dealbreaker: A Nonlinear Latent Variable Model for Educational Data
Authors: Andrew Lan, Tom Goldstein, Richard Baraniuk, Christoph Studer
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Statistical models of student responses on assessment questions, such as those in homeworks and exams, enable educators and computer-based personalized learning systems to gain insights into students’ knowledge using machine learning. Popular student-response models, including the Rasch model and item response theory models, represent the probability of a student answering a question correctly using an affine function of latent factors. While such models can accurately predict student responses, their ability to interpret the underlying knowledge structure (which is certainly nonlinear) is limited. In response, we develop a new, nonlinear latent variable model that we call the dealbreaker model, in which a student’s success probability is determined by their weakest concept mastery. We develop efficient parameter inference algorithms for this model using novel methods for nonconvex optimization. We show that the dealbreaker model achieves comparable or better prediction performance as compared to affine models with real-world educational datasets. We further demonstrate that the parameters learned by the dealbreaker model are interpretable—they provide key insights into which concepts are critical (i.e., the “dealbreaker”) to answering a question correctly. We conclude by reporting preliminary results for a movie-rating dataset, which illustrate the broader applicability of the dealbreaker model.
A Kernelized Stein Discrepancy for Goodness-of-fit Tests
Authors: Qiang Liu, Jason Lee, Michael Jordan
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein’s identity and the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic model fits a set of observations, and derive a new class of powerful goodness-of-fit tests that are widely applicable for complex and high dimensional distributions, even for those with computationally intractable normalization constants. Both theoretical and empirical properties of our methods are studied thoroughly.
Variable Elimination in the Fourier Domain
Authors: Yexiang Xue, Stefano Ermon, Ronan Le Bras,  Carla, Bart Selman
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major computational advantages. We explore a different type of compact representation based on discrete Fourier representations, complementing the classical approach based on conditional independencies. We show that a large class of probabilistic graphical models have a compact Fourier representation. This theoretical result opens up an entirely new way of approximating a probability distribution. We demonstrate the significance of this approach by applying it to the variable elimination algorithm. Compared with the traditional bucket representation and other approximate inference algorithms, we obtain significant improvements.
Low-Rank Matrix Approximation with Stability
Authors: Dongsheng Li, Chao Chen, Qin Lv, Junchi Yan, Li Shang, Stephen Chu
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Low-rank matrix approximation has been widely adopted in machine learning applications with sparse data, such as recommender systems. However, the sparsity of the data, incomplete and noisy, introduces challenges to the algorithm stability – small changes in the training data may significantly change the models. As a result, existing low-rank matrix approximation solutions yield low generalization performance, exhibiting high error variance on the training dataset, and minimizing the training error may not guarantee error reduction on the testing dataset. In this paper, we investigate the algorithm stability problem of low-rank matrix approximations. We present a new algorithm design framework, which (1) introduces new optimization objectives to guide stable matrix approximation algorithm design, and (2) solves the optimization problem to obtain stable low-rank approximation solutions with good generalization performance. Experimental results on real-world datasets demonstrate that the proposed work can achieve better prediction accuracy compared with both state-of-the-art low-rank matrix approximation methods and ensemble methods in recommendation task.
Linking losses for density ratio and class-probability estimation
Authors: Aditya Menon, Cheng Soon Ong
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Given samples from two densities p and q, density ratio estimation (DRE) is the problem of estimating the ratio p/q. Two popular discriminative approaches to DRE are KL importance estimation (KLIEP), and least squares importance fitting (LSIF). In this paper, we show that KLIEP and LSIF both employ class-probability estimation (CPE) losses. Motivated by this, we formally relate DRE and CPE, and demonstrate the viability of using existing losses from one problem for the other. For the DRE problem, we show that essentially any CPE loss (eg logistic, exponential) can be used, as this equivalently minimises a Bregman divergence to the true density ratio. We show how different losses focus on accurately modelling different ranges of the density ratio, and use this to design new CPE losses for DRE. For the CPE problem, we argue that the LSIF loss is useful in the regime where one wishes to rank instances with maximal accuracy at the head of the ranking. In the course of our analysis, we establish a Bregman divergence identity that may be of independent interest.
Stochastic Variance Reduction for Nonconvex Optimization
Authors: Sashank J. Reddi, Ahmed Hefny, Suvrit Sra, Barnabas Poczos, Alex Smola
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient descent (SGD); but their theoretical analysis almost exclusively assumes convexity. In contrast, we prove non-asymptotic rates of convergence (to stationary points) of SVRG for nonconvex optimization, and show that it is provably faster than SGD and gradient descent. We also analyze a subclass of nonconvex problems on which SVRG attains linear convergence to the global optimum. We extend our analysis to mini-batch variants of SVRG, showing (theoretical) linear speedup due to minibatching in parallel settings.
Hierarchical Variational Models
Authors: Rajesh Ranganath, Dustin Tran, David Blei
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive variational distribution that maintains efficient computation? To address this, we develop hierarchical variational models (HVMs). HVMs augment a variational approximation with a prior on its parameters, which allows it to capture complex structure for both discrete and continuous latent variables. The algorithm we develop is black box, can be used for any HVM, and has the same computational efficiency as the original approximation. We study HVMs on a variety of deep discrete latent variable models. HVMs generalize other expressive variational distributions and maintains higher fidelity to the posterior.
Hierarchical Span-Based Conditional Random Fields for Labeling and Segmenting Events in Wearable Sensor Data Streams
Authors: Roy Adams, Nazir Saleheen, Edison Thomaz, Abhinav Parate, Santosh Kumar, Benjamin Marlin
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The field of mobile health (mHealth) has the potential to yield new insights into health and behavior through the analysis of continuously recorded data from wearable health and activity sensors. In this paper, we present a hierarchical span-based conditional random field model for the key problem of jointly detecting discrete events in such sensor data streams and segmenting these events into high-level activity sessions. Our model includes higher-order cardinality factors and inter-event duration factors to capture domain-specific structure in the label space. We show that our model supports exact MAP inference in quadratic time via dynamic programming, which we leverage to perform learning in the structured support vector machine framework. We apply the model to the problems of smoking and eating detection using four real data sets. Our results show statistically significant improvements in segmentation performance relative to a hierarchical pairwise CRF.