Independent Component Analysis (ICA) was introduced in the 1980's as a model for Blind Source Separation (BSS), which refers to the process of recovering the sources underlying a mixture of signals, with little knowledge about the source signals or the mixing process. While there are many sophisticated algorithms for estimation, different methods have different shortcomings. In this paper, we develop a nonparametric score to adaptively pick the right algorithm for ICA with arbitrary Gaussian noise. The novelty of this score stems from the fact that it just assumes a finite second moment of the data and uses the characteristic function to evaluate the quality of the estimated mixing matrix without any knowledge of the parameters of the noise distribution. In addition, we propose some new contrast functions and algorithms that enjoy the same fast computability as existing algorithms like FASTICA and JADE but work in domains where the former may fail. While these also may have weaknesses, our proposed diagnostic, as shown by our simulations, can remedy them. Finally, we propose a theoretical framework to analyze the local and global convergence properties of our algorithms.

Link prediction and clustering are key problems for network-structureddata. While spectral clustering has strong theoretical guaranteesunder the popular stochastic blockmodel formulation of networks, itcan be expensive for large graphs. On the other hand, the heuristic ofpredicting links to nodes that share the most common neighbors withthe query node is much fast, and works very well in practice. We showtheoretically that the common neighbors heuristic can extract clustersw.h.p. when the graph is dense enough, and can do so even in sparsergraphs with the addition of a ``cleaning'' step. Empirical results onsimulated and real-world data support our conclusions.

BACKGROUND: The correlation between the expression levels of transcription factors and their target genes can be used to infer interactions within animal regulatory networks, but current methods are limited in their ability to make correct predictions. RESULTS: Here we describe a novel approach which uses nonparametric statistics to generate ordinary differential equation (ODE) models from expression data. Compared to other dynamical methods, our approach requires minimal information about the mathematical structure of the ODE; it does not use qualitative descriptions of interactions within the network; and it employs new statistics to protect against over-fitting. It generates spatio-temporal maps of factor activity, highlighting the times and spatial locations at which different regulators might affect target gene expression levels. We identify an ODE model for eve mRNA pattern formation in the Drosophila melanogaster blastoderm and show that this reproduces the experimental patterns well. Compared to a non-dynamic, spatial-correlation model, our ODE gives 59% better agreement to the experimentally measured pattern. Our model suggests that protein factors frequently have the potential to behave as both an activator and inhibitor for the same cis-regulatory module depending on the factors' concentration, and implies different modes of activation and repression. CONCLUSIONS: Our method provides an objective quantification of the regulatory potential of transcription factors in a network, is suitable for both low- and moderate-dimensional gene expression datasets, and includes improvements over existing dynamic and static models.

Local linearization techniques are an important class of nonparametric system identification. Identifying local linearizations in practice involves solving a linear regression problem that is ill-posed. The problem can be ill-posed either if the dynamics of the system lie on a manifold of lower dimension than the ambient space or if there are not enough measurements of all the modes of the dynamics of the system. We describe a set of linear regression estimators that can handle data lying on a lower-dimension manifold. These estimators differ from previous estimators, because these estimators are able to improve estimator performance by exploiting the sparsity of the system - the existence of direct interconnections between only some of the states - and can work in the ldquolarge p, small nrdquo setting in which the number of states is comparable to the number of data points. We describe our system identification procedure, which consists of a pre smoothing step and a regression step, and then we apply this procedure to data taken from a quadrotor helicopter. We use this data set to compare our procedure with existing procedures.

We give a review of various aspects of boosting, clarifying the issues through a few simple results, and relate our work and that of others to the minimax paradigm of statistics. We consider the population version of the boosting algorithm and prove its convergence to the Bayes classifier as a corollary of a general result about Gauss-Southwell optimization in Hilbert space. We then investigate the algorithmic convergence of the sample version, and give bounds to the time until perfect separation of the sample. We conclude by some results on the statistical optimality of the L2 boosting.

We propose a new method for estimating intrinsic dimension of a dataset derived by applying the principle of maximum likelihood to the distances between close neighbors. We derive the estimator by a Poisson process approximation, assess its bias and variance theo- retically and by simulations, and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators.

The Earth Mover's distanc1e was first introduced as a purely empirical ways to measure texture and color similarities. We show that it has a rigorous probabilistic interpretation and is conceptually equivalent to the Mallows distance on probability distributions. The two distances are exactly the same when applied to probability distributions, but behave differently when applied to unnormalized distributions with different masses, called signatures. We discuss the advantages and disadvantages of both distances, and statistical issues involved in computing them from data. We also report some texture classification results for the Mallows distance applied to texture features and compare several ways of estimating feature distributions. In addition, we list some known probabilistic properties of this distance.

The authors discuss the effect of having a finite number of detectors on the estimation of a bounded linear functional of a PET image. They argue that the functional should be estimated directly from the detector counts and give an estimate of the effect of the binning of the counts to order D(-2), where D is the number of detectors. The authors then suggest an estimator that includes a data determined bias correction reducing the bias to o(D(-2)).