Machine Learning

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A Kernel Theory of Modern Data Augmentation (1803.06084v2)

Tri Dao, Albert Gu, Alexander J. Ratner, Virginia Smith, Christopher De Sa, Christopher Ré

2018-03-16

Data augmentation, a technique in which a training set is expanded with class-preserving transformations, is ubiquitous in modern machine learning pipelines. In this paper, we seek to establish a theoretical framework for understanding data augmentation. We approach this from two directions: First, we provide a general model of augmentation as a Markov process, and show that kernels appear naturally with respect to this model, even when we do not employ kernel classification. Next, we analyze more directly the effect of augmentation on kernel classifiers, showing that data augmentation can be approximated by first-order feature averaging and second-order variance regularization components. These frameworks both serve to illustrate the ways in which data augmentation affects the downstream learning model, and the resulting analyses provide novel connections between prior work in invariant kernels, tangent propagation, and robust optimization. Finally, we provide several proof-of-concept applications showing that our theory can be useful for accelerating machine learning workflows, such as reducing the amount of computation needed to train using augmented data, and predicting the utility of a transformation prior to training.

TATi-Thermodynamic Analytics ToolkIt: TensorFlow-based software for posterior sampling in machine learning applications (1903.08640v1)

Frederik Heber, Zofia Trstanova, Benedict Leimkuhler

2019-03-20

We describe a TensorFlow-based library for posterior sampling and exploration in machine learning applications. TATi, the Thermodynamic Analytics ToolkIt, implements algorithms for 2nd order (underdamped) Langevin dynamics and Hamiltonian Monte Carlo (HMC). It also allows for rapid prototyping of new sampling methods in pure Python and supports an ensemble framework for generating multiple trajectories in parallel, a capability that is demonstrated by the implementation of a recently proposed ensemble preconditioning sampling procedure. In addition to explaining the architecture of TATi and its connections with the TensorFlow framework, this article contains preliminary numerical experiments to explore the efficiency of posterior sampling strategies in ML applications, in comparison to standard training strategies. We provide a glimpse of the potential of the new toolkit by studying (and visualizing) the loss landscape of a neural network applied to the MNIST hand-written digits data set.

Combining Model and Parameter Uncertainty in Bayesian Neural Networks (1903.07594v2)

Aliaksandr Hubin, Geir Storvik

2019-03-18

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: Parameter and prediction uncertainty become easily available, facilitating rigid statistical analysis. Furthermore, prior knowledge can be incorporated. However so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In this paper we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Finally, we show that incorporating model uncertainty via Bayesian model averaging and Bayesian model selection allows to drastically sparsify the structure of BNNs without significant loss of predictive power.

Column2Vec: Structural Understanding via Distributed Representations of Database Schemas (1903.08621v1)

Michael J. Mior, Alexander G. Ororbia II

2019-03-20

We present Column2Vec, a distributed representation of database columns based on column metadata. Our distributed representation has several applications. Using known names for groups of columns (i.e., a table name), we train a model to generate an appropriate name for columns in an unnamed table. We demonstrate the viability of our approach using schema information collected from open source applications on GitHub.

Near Optimal Exploration-Exploitation in Non-Communicating Markov Decision Processes (1807.02373v2)

Ronan Fruit, Matteo Pirotta, Alessandro Lazaric

2018-07-06

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This leads to defining weakly-communicating or multi-chain MDPs. In this paper, we introduce \tucrl, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with communicating states, actions and possible communicating next states, we derive a regret bound, where is the diameter (i.e., the longest shortest path) of the communicating part of the MDP. This is in contrast with optimistic algorithms (e.g., UCRL, Optimistic PSRL) that suffer linear regret in weakly-communicating MDPs, as well as posterior sampling or regularised algorithms (e.g., REGAL), which require prior knowledge on the bias span of the optimal policy to bias the exploration to achieve sub-linear regret. We also prove that in weakly-communicating MDPs, no algorithm can ever achieve a logarithmic growth of the regret without first suffering a linear regret for a number of steps that is exponential in the parameters of the MDP. Finally, we report numerical simulations supporting our theoretical findings and showing how TUCRL overcomes the limitations of the state-of-the-art.

Contextual Bandits with Random Projection (1903.08600v1)

Xiaotian Yu

2019-03-20

Contextual bandits with linear payoffs, which are also known as linear bandits, provide a powerful alternative for solving practical problems of sequential decisions, e.g., online advertisements. In the era of big data, contextual data usually tend to be high-dimensional, which leads to new challenges for traditional linear bandits mostly designed for the setting of low-dimensional contextual data. Due to the curse of dimensionality, there are two challenges in most of the current bandit algorithms: the first is high time-complexity; and the second is extreme large upper regret bounds with high-dimensional data. In this paper, in order to attack the above two challenges effectively, we develop an algorithm of Contextual Bandits via RAndom Projection (\texttt{CBRAP}) in the setting of linear payoffs, which works especially for high-dimensional contextual data. The proposed \texttt{CBRAP} algorithm is time-efficient and flexible, because it enables players to choose an arm in a low-dimensional space, and relaxes the sparsity assumption of constant number of non-zero components in previous work. Besides, we provide a linear upper regret bound for the proposed algorithm, which is associated with reduced dimensions.

A Graph-structured Dataset for Wikipedia Research (1903.08597v1)

Nicolas Aspert, Volodymyr Miz, Benjamin Ricaud, Pierre Vandergheynst

2019-03-20

Wikipedia is a rich and invaluable source of information. Its central place on the Web makes it a particularly interesting object of study for scientists. Researchers from different domains used various complex datasets related to Wikipedia to study language, social behavior, knowledge organization, and network theory. While being a scientific treasure, the large size of the dataset hinders pre-processing and may be a challenging obstacle for potential new studies. This issue is particularly acute in scientific domains where researchers may not be technically and data processing savvy. On one hand, the size of Wikipedia dumps is large. It makes the parsing and extraction of relevant information cumbersome. On the other hand, the API is straightforward to use but restricted to a relatively small number of requests. The middle ground is at the mesoscopic scale when researchers need a subset of Wikipedia ranging from thousands to hundreds of thousands of pages but there exists no efficient solution at this scale. In this work, we propose an efficient data structure to make requests and access subnetworks of Wikipedia pages and categories. We provide convenient tools for accessing and filtering viewership statistics or "pagecounts" of Wikipedia web pages. The dataset organization leverages principles of graph databases that allows rapid and intuitive access to subgraphs of Wikipedia articles and categories. The dataset and deployment guidelines are available on the LTS2 website \url{https://lts2.epfl.ch/Datasets/Wikipedia/}.

Data Augmentation for Leaf Segmentation and Counting Tasks in Rosette Plants (1903.08583v1)

Dmitry Kuznichov, Alon Zvirin, Yaron Honen, Ron Kimmel

2019-03-20

Deep learning techniques involving image processing and data analysis are constantly evolving. Many domains adapt these techniques for object segmentation, instantiation and classification. Recently, agricultural industries adopted those techniques in order to bring automation to farmers around the globe. One analysis procedure required for automatic visual inspection in this domain is leaf count and segmentation. Collecting labeled data from field crops and greenhouses is a complicated task due to the large variety of crops, growth seasons, climate changes, phenotype diversity, and more, especially when specific learning tasks require a large amount of labeled data for training. Data augmentation for training deep neural networks is well established, examples include data synthesis, using generative semi-synthetic models, and applying various kinds of transformations. In this paper we propose a method that preserves the geometric structure of the data objects, thus keeping the physical appearance of the data-set as close as possible to imaged plants in real agricultural scenes. The proposed method provides state of the art results when applied to the standard benchmark in the field, namely, the ongoing Leaf Segmentation Challenge hosted by Computer Vision Problems in Plant Phenotyping.

Support Estimation via Regularized and Weighted Chebyshev Approximations (1901.07506v3)

I, Chien, Olgica Milenkovic

2019-01-22

We introduce a new framework for estimating the support size of an unknown distribution which improves upon known approximation-based techniques. Our main contributions include describing a rigorous new weighted Chebyshev polynomial approximation method and introducing regularization terms into the problem formulation that provably improve the performance of state-of-the-art approximation-based approaches. In particular, we present both theoretical and computer simulation results that illustrate the utility and performance improvements of our method. The theoretical analysis relies on jointly optimizing the bias and variance components of the risk, and combining new weighted minmax polynomial approximation techniques with discretized semi-infinite programming solvers. Such a setting allows for casting the estimation problem as a linear program (LP) with a small number of variables and constraints that may be solved as efficiently as the original Chebyshev approximation-based problem. The described approach also applies to the support coverage and entropy estimation problems. Our newly developed technique is tested on synthetic data and used to estimate the number of bacterial species in the human gut. On synthetic datasets, we observed up to five-fold improvements in the value of the worst-case risk. For the bioinformatics application, metagenomic data from the NIH Human Gut and the American Gut Microbiome was combined and processed to obtain lists of bacterial taxonomies. These were subsequently used to compute the bacterial species histograms and estimate the number of bacterial species in the human gut to roughly 2350, with the species being represented by trillions of cells.

Rapid Convergence of the Unadjusted Langevin Algorithm: Log-Sobolev Suffices (1903.08568v1)

Santosh S. Vempala, Andre Wibisono

2019-03-20

We prove a convergence guarantee on the unadjusted Langevin algorithm for sampling assuming only that the target distribution satisfies a log-Sobolev inequality and the Hessian of is bounded. In particular, is not required to be convex or have higher derivatives bounded.

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