OpenRaiser/Intern-Atlas huggingface dataset:
Adding vs. Averaging in Distributed Primal-Dual Optimization
Venue: Conference ICML 2015
Year: 2015

Distributed optimization methods for large-scale machine learning suffer from a communication bottleneck. It is difficult to reduce this bottleneck while still efficiently and accurately aggregating partial work from different machines. In this paper, we present a novel generalization of the recent communication-efficient primal-dual framework (CoCoA) for distributed optimization. Our framework, CoCoA+, allows for additive combination of local updates to the global parameters at each iteration, whereas previous schemes with convergence guarantees only allow conservative averaging. We give stronger (primal-dual) convergence rate guarantees for both CoCoA as well as our new variants, and generalize the theory for both methods to cover non-smooth convex loss functions. We provide an extensive experimental comparison that shows the markedly improved performance of CoCoA+ on several real-world distributed datasets, especially when scaling up the number of machines.
Fixed-point algorithms for learning determinantal point processes
Venue: Conference ICML 2015
Year: 2015

Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key to learning DPPs from observed data. We consider the task of learning the DPP kernel, and develop for it a surprisingly simple yet effective new algorithm. Our algorithm offers the following benefits over previous approaches: (a) it is much simpler; (b) it yields equally good and sometimes even better local maxima; and (c) it runs an order of magnitude faster on large problems. We present experimental results on both real and simulated data to illustrate the numerical performance of our technique.
Rademacher Observations, Private Data, and Boosting
Venue: Conference ICML 2015
Year: 2015

The minimization of the logistic loss is a popular approach to batch supervised learning. Our paper starts from the surprising observation that, when fitting linear (or kernelized) classifiers, the minimization of the logistic loss is \textit{equivalent} to the minimization of an exponential \textit{rado}-loss computed (i) over transformed data that we call Rademacher observations (rados), and (ii) over the \textit{same} classifier as the one of the logistic loss. Thus, a classifier learnt from rados can be \textit{directly} used to classify \textit{observations}. We provide a learning algorithm over rados with boosting-compliant convergence rates on the \textit{logistic loss} (computed over examples). Experiments on domains with up to millions of examples, backed up by theoretical arguments, display that learning over a small set of random rados can challenge the state of the art that learns over the \textit{complete} set of examples. We show that rados comply with various privacy requirements that make them good candidates for machine learning in a privacy framework. We give several algebraic, geometric and computational hardness results on reconstructing examples from rados. We also show how it is possible to craft, and efficiently learn from, rados in a differential privacy framework. Tests reveal that learning from differentially private rados can compete with learning from random rados, and hence with batch learning from examples, achieving non-trivial privacy vs accuracy tradeoffs.
Learning Program Embeddings to Propagate Feedback on Student Code
Venue: Conference ICML 2015
Year: 2015

Providing feedback, both assessing final work and giving hints to stuck students, is difficult for open-ended assignments in massive online classes which can range from thousands to millions of students. We introduce a neural network method to encode programs as a linear mapping from an embedded precondition space to an embedded postcondition space and propose an algorithm for feedback at scale using these linear maps as features. We apply our algorithm to assessments from the Code.org Hour of Code and Stanford University's CS1 course, where we propagate human comments on student assignments to orders of magnitude more submissions.
Inferring Graphs from Cascades: A Sparse Recovery Framework
Venue: Conference ICML 2015
Year: 2015

In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph. In this paper, we approach this problem from the sparse recovery perspective. We introduce a general model of cascades, including the voter model and the independent cascade model, for which we provide the first algorithm which recovers the graph's edges with high probability and $O(s\log m)$ measurements where $s$ is the maximum degree of the graph and $m$ is the number of nodes. Furthermore, we show that our algorithm also recovers the edge weights (the parameters of the diffusion process) and is robust in the context of approximate sparsity. Finally we prove an almost matching lower bound of $Ω(s\log\frac{m}{s})$ and validate our approach empirically on synthetic graphs.
Global Convergence of Stochastic Gradient Descent for Some Non-convex Matrix Problems
Venue: Conference ICML 2015
Year: 2015

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a low-rank least-squares problem, and we prove that, under broad sampling conditions, our method converges globally from a random starting point within $O(ε^{-1} n \log n)$ steps with constant probability for constant-rank problems. Our modification of SGD relates it to stochastic power iteration. We also show experiments to illustrate the runtime and convergence of the algorithm.
Approval Voting and Incentives in Crowdsourcing
Venue: Conference ICML 2015
Year: 2015

The growing need for labeled training data has made crowdsourcing an important part of machine learning. The quality of crowdsourced labels is, however, adversely affected by three factors: (1) the workers are not experts; (2) the incentives of the workers are not aligned with those of the requesters; and (3) the interface does not allow workers to convey their knowledge accurately, by forcing them to make a single choice among a set of options. In this paper, we address these issues by introducing approval voting to utilize the expertise of workers who have partial knowledge of the true answer, and coupling it with a ("strictly proper") incentive-compatible compensation mechanism. We show rigorous theoretical guarantees of optimality of our mechanism together with a simple axiomatic characterization. We also conduct preliminary empirical studies on Amazon Mechanical Turk which validate our approach.
Telling cause from effect in deterministic linear dynamical systems
Venue: Conference ICML 2015
Year: 2015

Inferring a cause from its effect using observed time series data is a major challenge in natural and social sciences. Assuming the effect is generated by the cause trough a linear system, we propose a new approach based on the hypothesis that nature chooses the "cause" and the "mechanism that generates the effect from the cause" independent of each other. We therefore postulate that the power spectrum of the time series being the cause is uncorrelated with the square of the transfer function of the linear filter generating the effect. While most causal discovery methods for time series mainly rely on the noise, our method relies on asymmetries of the power spectral density properties that can be exploited even in the context of deterministic systems. We describe mathematical assumptions in a deterministic model under which the causal direction is identifiable with this approach. We also discuss the method's performance under the additive noise model and its relationship to Granger causality. Experiments show encouraging results on synthetic as well as real-world data. Overall, this suggests that the postulate of Independence of Cause and Mechanism is a promising principle for causal inference on empirical time series.
A Stochastic PCA and SVD Algorithm with an Exponential Convergence Rate
Venue: Conference ICML 2015
Year: 2015

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In contrast, existing algorithms suffer either from slow convergence, or computationally intensive iterations whose runtime scales with the data size. The algorithm builds on a recent variance-reduced stochastic gradient technique, which was previously analyzed for strongly convex optimization, whereas here we apply it to an inherently non-convex problem, using a very different analysis.
Deep Unsupervised Learning using Nonequilibrium Thermodynamics
Venue: Conference ICML 2015
Year: 2015

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.
Learning Fast-Mixing Models for Structured Prediction
Venue: Conference ICML 2015
Year: 2015

Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we define a new model family using strong Doeblin Markov chains, whose mixing times can be precisely controlled by a parameter. We also develop an algorithm to learn such models, which involves maximizing the data likelihood under the induced stationary distribution of these chains. We show empirical improvements on two challenging inference tasks.
Counterfactual Risk Minimization: Learning from Logged Bandit Feedback
Venue: Conference ICML 2015
Year: 2015

We develop a learning principle and an efficient algorithm for batch learning from logged bandit feedback. This learning setting is ubiquitous in online systems (e.g., ad placement, web search, recommendation), where an algorithm makes a prediction (e.g., ad ranking) for a given input (e.g., query) and observes bandit feedback (e.g., user clicks on presented ads). We first address the counterfactual nature of the learning problem through propensity scoring. Next, we prove generalization error bounds that account for the variance of the propensity-weighted empirical risk estimator. These constructive bounds give rise to the Counterfactual Risk Minimization (CRM) principle. We show how CRM can be used to derive a new learning method -- called Policy Optimizer for Exponential Models (POEM) -- for learning stochastic linear rules for structured output prediction. We present a decomposition of the POEM objective that enables efficient stochastic gradient optimization. POEM is evaluated on several multi-label classification problems showing substantially improved robustness and generalization performance compared to the state-of-the-art.
Learning Scale-Free Networks by Dynamic Node Specific Degree Prior
Venue: Conference ICML 2015
Year: 2015

Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks. The prior not only favors a desirable global node degree distribution, but also takes into consideration the relative strength of all the possible edges adjacent to the same node and the estimated degree of each individual node. To fulfill this, ranking is incorporated into the prior, which makes the problem challenging to solve. We employ an ADMM (alternating direction method of multipliers) framework to solve the Gaussian Graphical model regularized by this prior. Our experiments on both synthetic and real data show that our prior not only yields a scale-free network, but also produces many more correctly predicted edges than the others such as the scale-free inducing prior, the hub-inducing prior and the $l_1$ norm.
Modeling Order in Neural Word Embeddings at Scale
Venue: Conference ICML 2015
Year: 2015

Natural Language Processing (NLP) systems commonly leverage bag-of-words co-occurrence techniques to capture semantic and syntactic word relationships. The resulting word-level distributed representations often ignore morphological information, though character-level embeddings have proven valuable to NLP tasks. We propose a new neural language model incorporating both word order and character order in its embedding. The model produces several vector spaces with meaningful substructure, as evidenced by its performance of 85.8% on a recent word-analogy task, exceeding best published syntactic word-analogy scores by a 58% error margin. Furthermore, the model includes several parallel training methods, most notably allowing a skip-gram network with 160 billion parameters to be trained overnight on 3 multi-core CPUs, 14x larger than the previous largest neural network.
Safe Screening for Multi-Task Feature Learning with Multiple Data Matrices
Venue: Conference ICML 2015
Year: 2015

Multi-task feature learning (MTFL) is a powerful technique in boosting the predictive performance by learning multiple related classification/regression/clustering tasks simultaneously. However, solving the MTFL problem remains challenging when the feature dimension is extremely large. In this paper, we propose a novel screening rule---that is based on the dual projection onto convex sets (DPC)---to quickly identify the inactive features---that have zero coefficients in the solution vectors across all tasks. One of the appealing features of DPC is that: it is safe in the sense that the detected inactive features are guaranteed to have zero coefficients in the solution vectors across all tasks. Thus, by removing the inactive features from the training phase, we may have substantial savings in the computational cost and memory usage without sacrificing accuracy. To the best of our knowledge, it is the first screening rule that is applicable to sparse models with multiple data matrices. A key challenge in deriving DPC is to solve a nonconvex problem. We show that we can solve for the global optimum efficiently via a properly chosen parametrization of the constraint set. Moreover, DPC has very low computational cost and can be integrated with any existing solvers. We have evaluated the proposed DPC rule on both synthetic and real data sets. The experiments indicate that DPC is very effective in identifying the inactive features---especially for high dimensional data---which leads to a speedup up to several orders of magnitude.
Learning Parametric-Output HMMs with Two Aliased States
Venue: Conference ICML 2015
Year: 2015

In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations.
Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
Venue: Conference ICML 2015
Year: 2015

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling.
Theory of Dual-sparse Regularized Randomized Reduction
Venue: Conference ICML 2015
Year: 2015

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge on strong assumptions about the data, e.g., low rank of the data matrix or a large separable margin of classification, which hinder their applications in broad domains. To address these limitations, we propose dual-sparse regularized randomized reduction methods that introduce a sparse regularizer into the reduced dual problem. Under a mild condition that the original dual solution is a (nearly) sparse vector, we show that the resulting dual solution is close to the original dual solution and concentrates on its support set. In numerical experiments, we present an empirical study to support the analysis and we also present a novel application of the dual-sparse regularized randomized reduction methods to reducing the communication cost of distributed learning from large-scale high-dimensional data.
Distributed Estimation of Generalized Matrix Rank: Efficient Algorithms and Lower Bounds
Venue: Conference ICML 2015
Year: 2015

We study the following generalized matrix rank estimation problem: given an $n \times n$ matrix and a constant $c \geq 0$, estimate the number of eigenvalues that are greater than $c$. In the distributed setting, the matrix of interest is the sum of $m$ matrices held by separate machines. We show that any deterministic algorithm solving this problem must communicate $Ω(n^2)$ bits, which is order-equivalent to transmitting the whole matrix. In contrast, we propose a randomized algorithm that communicates only $\widetilde O(n)$ bits. The upper bound is matched by an $Ω(n)$ lower bound on the randomized communication complexity. We demonstrate the practical effectiveness of the proposed algorithm with some numerical experiments.
On the Relationship between Sum-Product Networks and Bayesian Networks
Venue: Conference ICML 2015
Year: 2015

In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the local conditional probability distributions at each node in the resulting BN by exploiting context-specific independence (CSI). The generated BN has a simple directed bipartite graphical structure. We show that by applying the Variable Elimination algorithm (VE) to the generated BN with ADD representations, we can recover the original SPN where the SPN can be viewed as a history record or caching of the VE inference process. To help state the proof clearly, we introduce the notion of {\em normal} SPN and present a theoretical analysis of the consistency and decomposability properties. We conclude the paper with some discussion of the implications of the proof and establish a connection between the depth of an SPN and a lower bound of the tree-width of its corresponding BN.
Low-Rank Matrix Recovery from Row-and-Column Affine Measurements
Venue: Conference ICML 2015
Year: 2015

We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix $X$. This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix recovery problems do not perform well in our case, hence the need for developing new algorithms and theory for our problem. We propose a simple algorithm for the problem based on Singular Value Decomposition ($SVD$) and least-squares ($LS$), which we term \alg. We prove that (a simplified version of) our algorithm can recover $X$ exactly with the minimum possible number of measurements in the noiseless case. In the general noisy case, we prove performance guarantees on the reconstruction accuracy under the Frobenius norm. In simulations, our row-and-column design and \alg algorithm show improved speed, and comparable and in some cases better accuracy compared to standard measurements designs and algorithms. Our theoretical and experimental results suggest that the proposed row-and-column affine measurements scheme, together with our recovery algorithm, may provide a powerful framework for affine matrix reconstruction.
Cumulative Prospect Theory Meets Reinforcement Learning: Prediction and Control
Venue: Conference ICML 2016
Year: 2016

Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent risk measures. We bring this idea to a risk-sensitive reinforcement learning (RL) setting and design algorithms for both estimation and control. The RL setting presents two particular challenges when CPT is applied: estimating the CPT objective requires estimations of the entire distribution of the value function and finding a randomized optimal policy. The estimation scheme that we propose uses the empirical distribution to estimate the CPT-value of a random variable. We then use this scheme in the inner loop of a CPT-value optimization procedure that is based on the well-known simulation optimization idea of simultaneous perturbation stochastic approximation (SPSA). We provide theoretical convergence guarantees for all the proposed algorithms and also illustrate the usefulness of CPT-based criteria in a traffic signal control application.