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Search Results: 1 - 10 of 1228 matches for " Junier Oliva "
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Fast Function to Function Regression
Junier Oliva,Willie Neiswanger,Barnabas Poczos,Eric Xing,Jeff Schneider
Computer Science , 2014,
Abstract: We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including time-series prediction problems, and also more general tasks like studying a mapping between two separate types of distributions. However, previous nonparametric estimators for FFR type problems scale badly computationally with the number of input/output pairs in a data-set. Given the complexity of a mapping between general functions it may be necessary to consider large data-sets in order to achieve a low estimation risk. To address this issue, we develop a novel scalable nonparametric estimator, the Triple-Basis Estimator (3BE), which is capable of operating over datasets with many instances. To the best of our knowledge, the 3BE is the first nonparametric FFR estimator that can scale to massive datasets. We analyze the 3BE's risk and derive an upperbound rate. Furthermore, we show an improvement of several orders of magnitude in terms of prediction speed and a reduction in error over previous estimators in various real-world data-sets.
Fast Distribution To Real Regression
Junier B. Oliva,Willie Neiswanger,Barnabas Poczos,Jeff Schneider,Eric Xing
Computer Science , 2013,
Abstract: We study the problem of distribution to real-value regression, where one aims to regress a mapping $f$ that takes in a distribution input covariate $P\in \mathcal{I}$ (for a non-parametric family of distributions $\mathcal{I}$) and outputs a real-valued response $Y=f(P) + \epsilon$. This setting was recently studied, and a "Kernel-Kernel" estimator was introduced and shown to have a polynomial rate of convergence. However, evaluating a new prediction with the Kernel-Kernel estimator scales as $\Omega(N)$. This causes the difficult situation where a large amount of data may be necessary for a low estimation risk, but the computation cost of estimation becomes infeasible when the data-set is too large. To this end, we propose the Double-Basis estimator, which looks to alleviate this big data problem in two ways: first, the Double-Basis estimator is shown to have a computation complexity that is independent of the number of of instances $N$ when evaluating new predictions after training; secondly, the Double-Basis estimator is shown to have a fast rate of convergence for a general class of mappings $f\in\mathcal{F}$.
Linear-time Learning on Distributions with Approximate Kernel Embeddings
Dougal J. Sutherland,Junier B. Oliva,Barnabás Póczos,Jeff Schneider
Computer Science , 2015,
Abstract: Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so through pairwise kernel evaluations between pdfs (or sample sets). While such an approach is fine for smaller datasets, the computation of an $N \times N$ Gram matrix is prohibitive in large datasets. Recent scalable estimators that work over pdfs have done so only with kernels that use Euclidean metrics, like the $L_2$ distance. However, there are a myriad of other useful metrics available, such as total variation, Hellinger distance, and the Jensen-Shannon divergence. This work develops the first random features for pdfs whose dot product approximates kernels using these non-Euclidean metrics, allowing estimators using such kernels to scale to large datasets by working in a primal space, without computing large Gram matrices. We provide an analysis of the approximation error in using our proposed random features and show empirically the quality of our approximation both in estimating a Gram matrix and in solving learning tasks in real-world and synthetic data.
Deep Mean Maps
Junier B. Oliva,Dougal J. Sutherland,Barnabás Póczos,Jeff Schneider
Computer Science , 2015,
Abstract: The use of distributions and high-level features from deep architecture has become commonplace in modern computer vision. Both of these methodologies have separately achieved a great deal of success in many computer vision tasks. However, there has been little work attempting to leverage the power of these to methodologies jointly. To this end, this paper presents the Deep Mean Maps (DMMs) framework, a novel family of methods to non-parametrically represent distributions of features in convolutional neural network models. DMMs are able to both classify images using the distribution of top-level features, and to tune the top-level features for performing this task. We show how to implement DMMs using a special mean map layer composed of typical CNN operations, making both forward and backward propagation simple. We illustrate the efficacy of DMMs at analyzing distributional patterns in image data in a synthetic data experiment. We also show that we extending existing deep architectures with DMMs improves the performance of existing CNNs on several challenging real-world datasets.
Bayesian Nonparametric Kernel-Learning
Junier Oliva,Avinava Dubey,Barnabas Poczos,Jeff Schneider,Eric P. Xing
Statistics , 2015,
Abstract: Kernel methods are ubiquitous tools in machine learning. They have proven to be effective in many domains and tasks. Yet, kernel methods often require the user to select a predefined kernel to build an estimator with. However, there is often little reason for the a priori selection of a kernel. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly effected by the choice of kernel. Furthermore, when directly applying kernel methods, one typically needs to compute a $N \times N$ Gram matrix of pairwise kernel evaluations to work with a dataset of $N$ instances. The computation of this Gram matrix precludes the direct application of kernel methods on large datasets. In this paper we introduce Bayesian nonparmetric kernel (BaNK) learning, a generic, data-driven framework for scalable learning of kernels. We show that this framework can be used for performing both regression and classification tasks and scale to large datasets. Furthermore, we show that BaNK outperforms several other scalable approaches for kernel learning on a variety of real world datasets.
FuSSO: Functional Shrinkage and Selection Operator
Junier B. Oliva,Barnabas Poczos,Timothy Verstynen,Aarti Singh,Jeff Schneider,Fang-Cheng Yeh,Wen-Yih Tseng
Computer Science , 2013,
Abstract: We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric assumptions about the nature of input functional covariates and assuming a linear form to the mapping of functional covariates to the response. We provide a statistical backing for use of the FuSSO via proof of asymptotic sparsistency under various conditions. Furthermore, we observe good results on both synthetic and real-world data.
Local energy approach to the dynamic glass transition
Ivan Junier
Physics , 2006, DOI: 10.1209/epl/i2006-10181-x
Abstract: We propose a new class of phenomenological models for dynamic glass transitions. The system consists of an ensemble of mesoscopic regions to which local energies are allocated. At each time step, a region is randomly chosen and a new local energy is drawn from a distribution that self-consistently depends on the global energy of the system. Then, the transition is accepted or not according to the Metropolis rule. Within this scheme, we model an energy threshold leading to a mode-coupling glass transition as in the p-spin model. The glassy dynamics is characterized by a two-step relaxation of the energy autocorrelation function. The aging scaling is fully determined by the evolution of the global energy and linear violations of the fluctuation dissipation relation are found for observables uncorrelated with the energies. Interestingly, our mean-field approach has a natural extension to finite dimension, that we briefly discuss.
Unstructured intermediate states in single protein force experiments
Ivan Junier,Felix Ritort
Physics , 2008, DOI: 10.1002/prot.21802
Abstract: Recent single-molecule force measurements on single-domain proteins have highlighted a three-state folding mechanism where a stabilized intermediate state (I) is observed on the folding trajectory between the stretched state and the native state. Here we investigate on-lattice protein-like heteropolymer models that lead to a three-state mechanism and show that force experiments can be useful to determine the structure of I. We have mostly found that I is composed of a core stabilized by a high number of native contacts, plus an unstructured extended chain. The lifetime of I is shown to be sensitive to modifications of the protein that spoil the core. We then propose three types of modifications--point mutations, cuts, and circular permutations--aiming at: (1) confirming the presence of the core and (2) determining its location, within one amino acid accuracy, along the polypeptide chain. We also propose force jump protocols aiming to probe the on/off-pathway nature of I.
Single-domain protein folding: a multi-faceted problem
Ivan Junier,Felix Ritort
Physics , 2008, DOI: 10.1063/1.2345624
Abstract: We review theoretical approaches, experiments and numerical simulations that have been recently proposed to investigate the folding problem in single-domain proteins. From a theoretical point of view, we emphasize the energy landscape approach. As far as experiments are concerned, we focus on the recent development of single-molecule techniques. In particular, we compare the results obtained with two main techniques: single protein force measurements with optical tweezers and single-molecule fluorescence in studies on the same protein (RNase H). This allows us to point out some controversial issues such as the nature of the denatured and intermediate states and possible folding pathways. After reviewing the various numerical simulation techniques, we show that on-lattice protein-like models can help to understand many controversial issues.
Tailoring symmetry groups using external alternate fields
I. Junier,J. Kurchan
Physics , 2002, DOI: 10.1209/epl/i2003-00583-2
Abstract: Macroscopic systems with continuous symmetries subjected to oscillatory fields have phases and transitions that are qualitatively different from their equilibrium ones. Depending on the amplitude and frequency of the fields applied, Heisenberg ferromagnets can become XY or Ising-like -or, conversely, anisotropies can be compensated -thus changing the nature of the ordered phase and the topology of defects. The phenomena can be viewed as a dynamic form of "order by disorder".
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