DimmWitted: A Study of Main-Memory Statistical Analytics

We perform the first study of the tradeoff space of access methods and replication to support statistical analytics using first-order methods executed in the main memory of a Non-Uniform Memory Access (NUMA) machine. Statistical analytics systems differ from conventional SQL-analytics in the amount and types of memory incoherence they can tolerate. Our goal is to understand tradeoffs in accessing the data in row- or column-order and at what granularity one should share the model and data for a statistical task. We study this new tradeoff space, and discover there are tradeoffs between hardware and statistical efficiency. We argue that our tradeoff study may provide valuable information for designers of analytics engines: for each system we consider, our prototype engine can run at least one popular task at least 100x faster. We conduct our study across five architectures using popular models including SVMs, logistic regression, Gibbs sampling, and neural networks

Aggregations over Generalized Hypertree Decompositions

We study a class of aggregate-join queries with multiple aggregation operators evaluated over annotated relations. We show that straightforward extensions of standard multiway join algorithms and generalized hypertree decompositions (GHDs) provide best-known runtime guarantees. In contrast, prior work uses bespoke algorithms and data structures and does not match these guarantees. Our extensions to the standard techniques are a pair of simple tests that (1) determine if two orderings of aggregation operators are equivalent and (2) determine if a GHD is compatible with a given ordering. These tests provide a means to find an optimal GHD that, when provided to standard join algorithms, will correctly answer a given aggregate-join query. The second class of our contributions is a pair of complete characterizations of (1) the set of orderings equivalent to a given ordering and (2) the set of GHDs compatible with some equivalent ordering. We show by example that previous approaches are incomplete. The key technical consequence of our characterizations is a decomposition of a compatible GHD into a set of (smaller) {\em unconstrained} GHDs, i.e. into a set of GHDs of sub-queries without aggregations. Since this decomposition is comprised of unconstrained GHDs, we are able to connect to the wide literature on GHDs for join query processing, thereby obtaining improved runtime bounds, MapReduce variants, and an efficient method to find approximately optimal GHDs

Ensuring Rapid Mixing and Low Bias for Asynchronous Gibbs Sampling

Gibbs sampling is a Markov chain Monte Carlo technique commonly used for estimating marginal distributions. To speed up Gibbs sampling, there has recently been interest in parallelizing it by executing asynchronously. While empirical results suggest that many models can be efficiently sampled asynchronously, traditional Markov chain analysis does not apply to the asynchronous case, and thus asynchronous Gibbs sampling is poorly understood. In this paper, we derive a better understanding of the two main challenges of asynchronous Gibbs: bias and mixing time. We show experimentally that our theoretical results match practical outcomes

Gaussian Quadrature for Kernel Features

Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel machines, but employing the randomized feature map means that $O(\epsilon^{-2})$ samples are required to achieve an approximation error of at most $\epsilon$. We investigate some alternative schemes for constructing feature maps that are deterministic, rather than random, by approximating the kernel in the frequency domain using Gaussian quadrature. We show that deterministic feature maps can be constructed, for any $\gamma > 0$, to achieve error $\epsilon$ with $O(e^{e^\gamma} + \epsilon^{-1/\gamma})$ samples as $\epsilon$ goes to 0. Our method works particularly well with sparse ANOVA kernels, which are inspired by the convolutional layer of CNNs. We validate our methods on datasets in different domains, such as MNIST and TIMIT, showing that deterministic features are faster to generate and achieve accuracy comparable to the state-of-the-art kernel methods based on random Fourier features.Comment: Neural Information Processing Systems (NIPS) 201

Asynchronous stochastic convex optimization

We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for asymptotic optimality of standard stochastic gradient procedures. Roughly, the noise inherent to the stochastic approximation scheme dominates any noise from asynchrony. We also give empirical evidence demonstrating the strong performance of asynchronous, parallel stochastic optimization schemes, demonstrating that the robustness inherent to stochastic approximation problems allows substantially faster parallel and asynchronous solution methods.Comment: 38 pages, 8 figure

A Measure of Dependence Between Discrete and Continuous Variables

Mutual Information (MI) is an useful tool for the recognition of mutual dependence berween data sets. Differen methods for the estimation of MI have been developed when both data sets are discrete or when both data sets are continuous. The MI estimation between a discrete data set and a continuous data set has not received so much attention. We present here a method for the estimation of MI for this last case based on the kernel density approximation. The calculation may be of interest in diverse contexts. Since MI is closely related to Jensen Shannon divergence, the method here developed is of particular interest in the problem of sequence segmentation

Understanding and Improving Information Transfer in Multi-Task Learning

We investigate multi-task learning approaches that use a shared feature representation for all tasks. To better understand the transfer of task information, we study an architecture with a shared module for all tasks and a separate output module for each task. We study the theory of this setting on linear and ReLU-activated models. Our key observation is that whether or not tasks' data are well-aligned can significantly affect the performance of multi-task learning. We show that misalignment between task data can cause negative transfer (or hurt performance) and provide sufficient conditions for positive transfer. Inspired by the theoretical insights, we show that aligning tasks' embedding layers leads to performance gains for multi-task training and transfer learning on the GLUE benchmark and sentiment analysis tasks; for example, we obtain a 2.35% GLUE score average improvement on 5 GLUE tasks over BERT-LARGE using our alignment method. We also design an SVD-based task reweighting scheme and show that it improves the robustness of multi-task training on a multi-label image dataset.Comment: Appeared in ICLR 202

Low-Precision Random Fourier Features for Memory-Constrained Kernel Approximation

We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical generalization performance of kernel approximation methods than conventional metrics. An important consequence of this definition is that a kernel approximation matrix must be high rank to attain close approximation. Because storing a high-rank approximation is memory intensive, we propose using a low-precision quantization of random Fourier features (LP-RFFs) to build a high-rank approximation under a memory budget. Theoretically, we show quantization has a negligible effect on generalization performance in important settings. Empirically, we demonstrate across four benchmark datasets that LP-RFFs can match the performance of full-precision RFFs and the Nystr\"{o}m method, with 3x-10x and 50x-460x less memory, respectively.Comment: International Conference on Artificial Intelligence and Statistics (AISTATS) 201

SwellShark: A Generative Model for Biomedical Named Entity Recognition without Labeled Data

We present SwellShark, a framework for building biomedical named entity recognition (NER) systems quickly and without hand-labeled data. Our approach views biomedical resources like lexicons as function primitives for autogenerating weak supervision. We then use a generative model to unify and denoise this supervision and construct large-scale, probabilistically labeled datasets for training high-accuracy NER taggers. In three biomedical NER tasks, SwellShark achieves competitive scores with state-of-the-art supervised benchmarks using no hand-labeled training data. In a drug name extraction task using patient medical records, one domain expert using SwellShark achieved within 5.1% of a crowdsourced annotation approach -- which originally utilized 20 teams over the course of several weeks -- in 24 hours

Asynchrony begets Momentum, with an Application to Deep Learning

Asynchronous methods are widely used in deep learning, but have limited theoretical justification when applied to non-convex problems. We show that running stochastic gradient descent (SGD) in an asynchronous manner can be viewed as adding a momentum-like term to the SGD iteration. Our result does not assume convexity of the objective function, so it is applicable to deep learning systems. We observe that a standard queuing model of asynchrony results in a form of momentum that is commonly used by deep learning practitioners. This forges a link between queuing theory and asynchrony in deep learning systems, which could be useful for systems builders. For convolutional neural networks, we experimentally validate that the degree of asynchrony directly correlates with the momentum, confirming our main result. An important implication is that tuning the momentum parameter is important when considering different levels of asynchrony. We assert that properly tuned momentum reduces the number of steps required for convergence. Finally, our theory suggests new ways of counteracting the adverse effects of asynchrony: a simple mechanism like using negative algorithmic momentum can improve performance under high asynchrony. Since asynchronous methods have better hardware efficiency, this result may shed light on when asynchronous execution is more efficient for deep learning systems.Comment: Full version of a paper published in Annual Allerton Conference on Communication, Control, and Computing (Allerton) 201