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Felix Agakov

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NeurIPS Conference 2010 Conference Paper

Sparse Instrumental Variables (SPIV) for Genome-Wide Studies

  • Paul Mckeigue
  • Jon Krohn
  • Amos Storkey
  • Felix Agakov

This paper describes a probabilistic framework for studying associations between multiple genotypes, biomarkers, and phenotypic traits in the presence of noise and unobserved confounders for large genetic studies. The framework builds on sparse linear methods developed for regression and modified here for inferring causal structures of richer networks with latent variables. The method is motivated by the use of genotypes as ``instruments'' to infer causal associations between phenotypic biomarkers and outcomes, without making the common restrictive assumptions of instrumental variable methods. The method may be used for an effective screening of potentially interesting genotype phenotype and biomarker-phenotype associations in genome-wide studies, which may have important implications for validating biomarkers as possible proxy endpoints for early stage clinical trials. Where the biomarkers are gene transcripts, the method can be used for fine mapping of quantitative trait loci (QTLs) detected in genetic linkage studies. The method is applied for examining effects of gene transcript levels in the liver on plasma HDL cholesterol levels for a sample of sequenced mice from a heterogeneous stock, with $\sim 10^5$ genetic instruments and $\sim 47 \times 10^3$ gene transcripts.

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NeurIPS Conference 2005 Conference Paper

Kernelized Infomax Clustering

  • David Barber
  • Felix Agakov

We propose a simple information-theoretic approach to soft clus- tering based on maximizing the mutual information I(x, y) between the unknown cluster labels y and the training patterns x with re- spect to parameters of specifically constrained encoding distribu- tions. The constraints are chosen such that patterns are likely to be clustered similarly if they lie close to specific unknown vectors in the feature space. The method may be conveniently applied to learning the optimal affinity matrix, which corresponds to learn- ing parameters of the kernelized encoder. The procedure does not require computations of eigenvalues of the Gram matrices, which makes it potentially attractive for clustering large data sets.

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NeurIPS Conference 2003 Conference Paper

Extreme Components Analysis

  • Max Welling
  • Christopher Williams
  • Felix Agakov

Principal components analysis (PCA) is one of the most widely used techniques in machine learning and data mining. Minor components analysis (MCA) is less well known, but can also play an important role in the presence of constraints on the data distribution. In this paper we present a probabilistic model for “extreme components analysis” (XCA) which at the maximum likelihood solution extracts an optimal combina- tion of principal and minor components. For a given number of compo- nents, the log-likelihood of the XCA model is guaranteed to be larger or equal than that of the probabilistic models for PCA and MCA. We de- scribe an efficient algorithm to solve for the globally optimal solution. For log-convex spectra we prove that the solution consists of principal components only, while for log-concave spectra the solution consists of minor components. In general, the solution admits a combination of both. In experiments we explore the properties of XCA on some synthetic and real-world datasets.

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NeurIPS Conference 2003 Conference Paper

Information Maximization in Noisy Channels : A Variational Approach

  • David Barber
  • Felix Agakov

The maximisation of information transmission over noisy channels is a common, albeit generally computationally difficult problem. We approach the difficulty of computing the mutual information for noisy channels by using a variational approximation. The re- sulting IM algorithm is analagous to the EM algorithm, yet max- imises mutual information, as opposed to likelihood. We apply the method to several practical examples, including linear compression, population encoding and CDMA.

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NeurIPS Conference 2001 Conference Paper

Products of Gaussians

  • Christopher Williams
  • Felix Agakov
  • Stephen Felderhof

Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data. Be(cid: 173) low we consider PoE models in which each expert is a Gaussian. Although the product of Gaussians is also a Gaussian, if each Gaus(cid: 173) sian has a simple structure the product can have a richer structure. We examine (1) Products of Gaussian pancakes which give rise to probabilistic Minor Components Analysis, (2) products of I-factor PPCA models and (3) a products of experts construction for an AR(l) process. Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data. In this paper we consider PoE models in which each expert is a Gaussian. It is easy to see that in this case the product model will also be Gaussian. However, if each Gaussian has a simple structure, the product can have a richer structure. Using Gaussian experts is attractive as it permits a thorough analysis of the product architecture, which can be difficult with other models, e. g. models defined over discrete random variables. Below we examine three cases of the products of Gaussians construction: (1) Prod(cid: 173) ucts of Gaussian pancakes (PoGP) which give rise to probabilistic Minor Compo(cid: 173) nents Analysis (MCA), providing a complementary result to probabilistic Principal Components Analysis (PPCA) obtained by Tipping and Bishop (1999); (2) Prod(cid: 173) ucts of I-factor PPCA models; (3) A products of experts construction for an AR(l) process. Products of Gaussians If each expert is a Gaussian pi(xI8i ) '" N(J1i' ( i), the resulting distribution of the product of m Gaussians may be expressed as By completing the square in the exponent it may be easily shown that p(xI8) N(/1; E, (2: ), where (E l = 2: :1 (i l. To simplify the following derivations we will assume that pi(xI8i ) '" N(O, (i) and thus that p(xI8) '" N(O, (2: ). J12: i ° can be obtained by translation of the coordinate system. 1 Products of Gaussian Pancakes A Gaussian "pancake" (GP) is a d-dimensional Gaussian, contracted in one dimen(cid: 173) sion and elongated in the other d - 1 dimensions. In this section we show that the maximum likelihood solution for a product of Gaussian pancakes (PoGP) yields a probabilistic formulation of Minor Components Analysis (MCA). 1. 1 Covariance Structure of a GP Expert Consider a d-dimensional Gaussian whose probability contours are contracted in the direction w and equally elongated in mutually orthogonal directions VI, .. ., vd-l. We call this a Gaussian pancake or GP. Its inverse covariance may be written as

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