We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to the first fully continuous optimization for score-based learning of DAG models parametrized by a linear structural equation model (SEM). We extend this algebraic characterization to nonparametric SEM by leveraging nonparametric sparsity based on partial derivatives, resulting in a continuous optimization problem that can be applied to a variety of nonparametric and semiparametric models including GLMs, additive noise models, and index models as special cases. Unlike existing approaches that require specific modeling choices, loss functions, or algorithms, we present a completely general framework that can be applied to general nonlinear models (e.g. without additive noise), general differentiable loss functions, and generic black-box optimization routines.

Personalized recommendation products at Twitter target a multitude of heterogeneous items: Tweets, Events, Topics, Hashtags, and users. Each of these targets varies in their cardinality (which affects the scale of the problem) and their "shelf life'' (which constrains the latency of generating the recommendations). Although Twitter has built a variety of recommendation systems before dating back a decade, solutions to the broader problem were mostly tackled piecemeal. In this paper, we present SimClusters, a general-purpose representation layer based on overlapping communities into which users as well as heterogeneous content can be captured as sparse, interpretable vectors to support a multitude of recommendation tasks. We propose a novel algorithm for community discovery based on Metropolis-Hastings sampling, which is both more accurate and significantly faster than off-the-shelf alternatives. SimClusters scales to networks with billions of users and has been effective across a variety of deployed applications at Twitter.

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: we formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree.

Machine learning (ML) algorithms are commonly applied to big data, using distributed systems that partition the data across machines and allow each machine to read and update all ML model parameters --- a strategy known as data parallelism. An alternative and complimentary strategy, model parallelism, partitions the model parameters for non-shared parallel access and updates, and may periodically repartition the parameters to facilitate communication. Model parallelism is motivated by two challenges that data-parallelism does not usually address: (1) parameters may be dependent, thus naive concurrent updates can introduce errors that slow convergence or even cause algorithm failure; (2) model parameters converge at different rates, thus a small subset of parameters can bottleneck ML algorithm completion. We propose scheduled model parallelism (SchMP), a programming approach that improves ML algorithm convergence speed by efficiently scheduling parameter updates, taking into account parameter dependencies and uneven convergence. To support SchMP at scale, we develop a distributed framework STRADS which optimizes the throughput of SchMP programs, and benchmark four common ML applications written as SchMP programs: LDA topic modeling, matrix factorization, sparse least-squares (Lasso) regression and sparse logistic regression. By improving ML progress per iteration through SchMP programming whilst improving iteration throughput through STRADS we show that SchMP programs running on STRADS outperform non-model-parallel ML implementations: for example, SchMP LDA and SchMP Lasso respectively achieve 10x and 5x faster convergence than recent, well-established baselines.

Regularization has played a key role in deriving sensible estimators in high dimensional statistical inference. A substantial amount of recent works has argued for nonconvex regularizers in favor of their superior theoretical properties and excellent practical performances. In a different but analogous vein, nonconvex loss functions are promoted because of their robustness against "outliers". However, these nonconvex formulations are computationally more challenging, especially in the presence of nonsmoothness and non-separability. To address this issue, we propose a new proximal gradient meta-algorithm by rigorously extending the proximal average to the nonconvex setting. We formally prove its nice convergence properties, and illustrate its effectiveness on two applications: multi-task graph-guided fused lasso and robust support vector machines. Experiments demonstrate that our method compares favorably against other alternatives.

How can one build a distributed framework that allows efficient deployment of a wide spectrum of modern advanced machine learning (ML) programs for industrial-scale problems using Big Models (100s of billions of parameters) on Big Data (terabytes or petabytes)- Contemporary parallelization strategies employ fine-grained operations and scheduling beyond the classic bulk-synchronous processing paradigm popularized by MapReduce, or even specialized operators relying on graphical representations of ML programs. The variety of approaches tends to pull systems and algorithms design in different directions, and it remains difficult to find a universal platform applicable to a wide range of different ML programs at scale. We propose a general-purpose framework that systematically addresses data- and model-parallel challenges in large-scale ML, by leveraging several fundamental properties underlying ML programs that make them different from conventional operation-centric programs: error tolerance, dynamic structure, and nonuniform convergence; all stem from the optimization-centric nature shared in ML programs' mathematical definitions, and the iterative-convergent behavior of their algorithmic solutions. These properties present unique opportunities for an integrative system design, built on bounded-latency network synchronization and dynamic load-balancing scheduling, which is efficient, programmable, and enjoys provable correctness guarantees. We demonstrate how such a design in light of ML-first principles leads to significant performance improvements versus well-known implementations of several ML programs, allowing them to run in much less time and at considerably larger model sizes, on modestly-sized computer clusters.

Topic models are effective probabilistic tools for processing large collections of unstructured data. With the exponential growth of modern industrial data, and consequentially also with our ambition to explore much bigger models, there is a real pressing need to significantly scale up topic modeling algorithms, which has been taken up in lots of previous works, culminating in the recent fast Markov chain Monte Carlo sampling algorithms in [10, 23] for the unsupervised latent Dirichlet allocation (LDA) formulations.

When building large-scale machine learning (ML) programs, such as massive topic models or deep neural networks with up to trillions of parameters and training examples, one usually assumes that such massive tasks can only be attempted with industrial-sized clusters with thousands of nodes, which are out of reach for most practitioners and academic researchers. We consider this challenge in the context of topic modeling on web-scale corpora, and show that with a modest cluster of as few as 8 machines, we can train a topic model with 1 million topics and a 1-million-word vocabulary (for a total of 1 trillion parameters), on a document collection with 200 billion tokens --- a scale not yet reported even with thousands of machines. Our major contributions include: 1) a new, highly-efficient O(1) Metropolis-Hastings sampling algorithm, whose running cost is (surprisingly) agnostic of model size, and empirically converges nearly an order of magnitude more quickly than current state-of-the-art Gibbs samplers; 2) a model-scheduling scheme to handle the big model challenge, where each worker machine schedules the fetch/use of sub-models as needed, resulting in a frugal use of limited memory capacity and network bandwidth; 3) a differential data-structure for model storage, which uses separate data structures for high- and low-frequency words to allow extremely large models to fit in memory, while maintaining high inference speed. These contributions are built on top of the Petuum open-source distributed ML framework, and we provide experimental evidence showing how this development puts massive data and models within reach on a small cluster, while still enjoying proportional time cost reductions with increasing cluster size.

What is a systematic way to efficiently apply a wide spectrum of advanced ML programs to industrial scale problems, using Big Models (up to 100 s of billions of parameters) on Big Data (up to terabytes or petabytes)? Modern parallelization strategies employ fine-grained operations and scheduling beyond the classic bulk-synchronous processing paradigm popularized by MapReduce, or even specialized graph-based execution that relies on graph representations of ML programs. The variety of approaches tends to pull systems and algorithms design in different directions, and it remains difficult to find a universal platform applicable to a wide range of ML programs at scale. We propose a general-purpose framework, Petuum, that systematically addresses data- and model-parallel challenges in large-scale ML, by observing that many ML programs are fundamentally optimization-centric and admit error-tolerant, iterative-convergent algorithmic solutions. This presents unique opportunities for an integrative system design, such as bounded-error network synchronization and dynamic scheduling based on ML program structure. We demonstrate the efficacy of these system designs versus well-known implementations of modern ML algorithms, showing that Petuum allows ML programs to run in much less time and at considerably larger model sizes, even on modestly-sized compute clusters.

Topic models have played a pivotal role in analyzing large collections of complex data. Besides discovering latent semantics, supervised topic models (STMs) can make predictions on unseen test data. By marrying with advanced learning techniques, the predictive strengths of STMs have been dramatically enhanced, such as max-margin supervised topic models, state-of-the-art methods that integrate max-margin learning with topic models. Though powerful, max-margin STMs have a hard non-smooth learning problem. Existing algorithms rely on solving multiple latent SVM subproblems in an EM-type procedure, which can be too slow to be applicable to large-scale categorization tasks.

Logistic-normal topic models can effectively discover correlation structures among latent topics. However, their inference remains a challenge because of the non-conjugacy between the logistic-normal prior and multinomial topic mixing proportions. Existing algorithms either make restricting mean-field assumptions or are not scalable to large-scale applications. This paper presents a partially collapsed Gibbs sampling algorithm that approaches the provably correct distribution by exploring the ideas of data augmentation. To improve time efficiency, we further present a parallel implementation that can deal with large-scale applications and learn the correlation structures of thousands of topics from millions of documents. Extensive empirical results demonstrate the promise.