ultra scalable and efficient methods for hybrid observational and experimental local causal pathway discovery discovery of causal relations from data is a fundamental objective of several scientific disciplines most causal discovery algorithms that use observational data can infer causality only up to a statistical equivalency class thus leaving many causal relations undetermined in general complete identification of causal relations requires experimentation to augment discoveries from observational data this has led to the recent development of several methods for active learning of causal networks that utilize both observational and experimental data in order to discover causal networks in this work we focus on the problem of discovering local causal pathways that contain only direct causes and direct effects of the target variable of interest and propose new discovery methods that aim to minimize the number of required experiments relax common sufficient discovery assumptions in order to increase discovery accuracy and scale to high dimensional data with thousands of variables we conduct a comprehensive evaluation of new and existing methods with data of dimensionality up to 1 000 000 variables we use both artificially simulated networks and in silico gene transcriptional networks that model the characteristics of real gene expression data

false discovery rate adjusted charting schemes for multistage process monitoring and fault identification most statistical process control research focuses on single stage processes this article considers the problem of multistage process monitoring and fault identification this problem is formulated as a multiple hypotheses testing problem however as the number of stages increases the detection power of multiple hypotheses testing methods that seek to control the type i error rate decreases dramatically to maintain the detection power we use a false discovery rate fdr control approach which is widely used in microarray research two multistage process monitoring and fault identification schemes an fdr adjusted shewhart chart and an fdr adjusted cumulative sum cusum chart are established to apply the fdr approach the distribution of the cusum statistics are obtained based on markov chain theory and brownian motion with drift models the detection and fault identification power of the new schemes are evaluated by the monte carlo method the results indicate that the novel fdr adjusted approaches

a provably secure short signature scheme based on discrete logarithms we propose a short signature scheme whose security is closely related to the discrete logarithm assumption in the random oracle model the new scheme offers a better security guarantee than existing discrete logarithm based signature schemes the main advantage of this scheme over the dsa signature scheme is that it has a one fourth reduction in both the signature length and the verification computation the level of security is preserved the new short signatures are needed to low bandwidth communication low storage and low computation environments and particularly applicable to smart cards and wireless devices

fluctuations convergence times correlation functions and power laws from many body lyapunov spectra for soft and hard disks and spheres the dynamical instability of many body systems is best characterized through the time dependent local lyapunov spectrum l j its associated comoving eigenvectors d j and the global time averaged spectrum l j we study the fluctuations of the local spectra as well as the convergence ratesand correlation functions associated with the d vectors as functions of j and system size n all the number dependences can be described by simple power laws the various powers depend on the thermodynamic state and force law as well as system dimensionality

lyapunov instabilities of lennard jones fluids recent work on many particle systems reveals the existence of regular collective perturbations corresponding to the smallest positive lyapunov exponents les called hydrodynamic lyapunov modes until now however these modes have been found only for hard core systems here we report results on lyapunov spectra and lyapunov vectors lvs for lennard jones fluids by considering the fourier transform of the coordinate fluctuation density u ensuremath alpha x t it is found that the lvs with ensuremath lambda ensuremath approx 0 are highly dominated by a few components with low wave numbers these numerical results provide strong evidence that hydrodynamic lyapunov modes do exist in soft potential systems although the collective lyapunov modes are more vague than in hard core systems in studying the density and temperature dependence of these modes it is found that when the value of the lyapunov exponent ensuremath lambda ensuremath alpha is plotted as function of the dominant wave number k mathit max of the corresponding lv all data from simulations with different densities and temperatures collapse onto a single curve this shows that the dispersion relation ensuremath lambda ensuremath alpha vs k mathit max for hydrodynamical lyapunov modes appears to be universal for the low density cases studied here despite the wavelike character of the lvs no steplike structure exists in the lyapunov spectrum of the systems studied here in contrast to the hard core case further numerical simulations show that the finite time les fluctuate strongly we have also investigated localization features of lvs and propose a length scale to characterize the hamiltonian spatiotemporal chaotic states

learning linear cyclic causal models with latent variables identifying cause effect relationships between variables of interest is a central problem in science given a set of experiments we describe a procedure that identifies linear models that may contain cycles and latent variables we provide a detailed description of the model family full proofs of the necessary and sufficient conditions for identifiability a search algorithm that is complete and a discussion of what can be done when the identifiability conditions are not satisfied the algorithm is comprehensively tested in simulations comparing it to competing algorithms in the literature furthermore we adapt the procedure to the problem of cellular network inference applying it to the biologically realistic data of the dreamchallenges the paper provides a full theoretical foundation for the causal discovery procedure first presented by eberhardt et al 2010 and hyttinen et al 2010

resampling based multiple testing methods with covariate adjustment application to investigation of antiretroviral drug susceptibility identifying genetic mutations that cause clinical resistance to antiretroviral drugs requires adjustment for potential confounders such as the number of active drugs in a hiv infected patient s regimen other than the one of interest motivated by this problem we investigated resampling based methods to test equal mean response across multiple groups defined by hiv genotype after adjustment for covariates we consider construction of test statistics and their null distributions under two types of model parametric and semiparametric the covariate function is explicitly specified in the parametric but not in the semiparametric approach the parametric approach is more precise when models are correctly specified but suffer from bias when they are not the semiparametric approach is more robust to model misspecification but may be less efficient to help preserve type i error while also improving power in both approaches we propose resampling approaches based on matching of observations with similar covariate values matching reduces the impact of model misspecification as well as imprecision in estimation these methods are evaluated via simulation studies and applied to a data set that combines results from a variety of clinical studies of salvage regimens our focus is on relating hiv genotype to viral susceptibility to abacavir after adjustment for the number of active antiretroviral drugs excluding abacavir in the patient s regimen

tests for high dimensional covariance matrices we propose tests for sphericity and identity of high dimensional covariance matrices the tests are nonparametric without assuming a specific parametric distribution for the data they can accommodate situations where the data dimension is much larger than the sample size namely the large p small n situations we demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes we applied the proposed test on a microarray dataset on yorkshire gilts and tested for the covariance structure for the expression levels for sets of genes

the false discovery rate for multiple testing in factorial experiments identifying the important factors and effects is an important goal in the analysis of two level fractional factorial experiments in moderate and large experiments the large number of potential effects presents problems of multiple statistical inference in this work we apply the false discovery rate fdr idea in multiple inference to effect identification in factorial experiments the fdr is the expected proportion of inert effects among those declared active which we believe is a more relevant quantity to control than the probability of a single erroneous declaration the criterion that has been adopted in previous studies we show how to combine the control of fdr with popular methods for estimating contrast standard error in unreplicated experiments we present simulations of unreplicated 16 and 32 run experiments that illustrate the improvements in power that can be obtained by controlling the fdr we also analyze data from an actual 128 run experiment with replication in which the fdr identifie

gene identification using true discovery rate degree of association sets and estimates corrected for regression to the mean analyses intended to identify genes with expression that is associated with some clinical outcome or state are often based on ranked p values from tests of point null hypotheses of no association van de wiel and kim take the innovative approach of testing the interval null hypotheses that the degree of association for a gene is less than some value of interest against the alternative that it is greater combining this idea with the false discovery rate controlling methods of storey taylor and siegmund gives a computationally simple way to identify true discovery rate degree of association tdrda sets of genes among which a specified proportion are expected to have an absolute association of a specified degree or more this leads to a gene ranking method that uses the maximum lower bound degree of association for which each gene belongs to a tdrda set estimates of each gene s actual degree of association with approximate correction for selection bias due to regression to the mean rm can be derived using simple bivariate normal theory and efron and tibshirani s empirical bayes approach for a given data set all possible tdrda sets can be displayed along with the gene ranking and the rm corrected estimates of degree of association in a concise graphical summary

false discovery control in large scale spatial multiple testing summary the paper develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals we consider both pointwise and clusterwise spatial analyses and derive oracle procedures which optimally control the false discovery rate false discovery exceedance and false cluster rate a data driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain our multiple testing procedures are asymptotically valid and can be effectively implemented using bayesian computational algorithms for analysis of large spatial data sets numerical results show that the procedures proposed lead to more accurate error control and better power performance than conventional methods we demonstrate our methods for analysing the time trends in tropospheric ozone in eastern usa

false discovery rate control with groups in the context of large scale multiple hypothesis testing the hypotheses often possess certain group structures based on additional information such as gene ontology in gene expression data and phenotypes in genome wide association studies it is hence desirable to incorporate such information when dealing with multiplicity problems to increase statistical power in this article we demonstrate the benefit of considering group structure by presenting a p value weighting procedure which utilizes the relative importance of each group while controlling the false discovery rate under weak conditions the procedure is easy to implement and shown to be more powerful than the classical benjamini hochberg procedure in both theoretical and simulation studies by estimating the proportion of true null hypotheses the data driven procedure controls the false discovery rate asymptotically our analysis on one breast cancer dataset confirms that the procedure performs favorably compared with the classical method

non restarting cumulative sum charts and control of the false discovery rate cumulative sum or cusum charts are typically used to detect a change in the distribution of a sequence of observations e g shifts in the mean usually after signalling the chart is restarted by setting it to some value below the signalling threshold we propose a non restarting cusum chart which is able to detect periods during which the stream is out of control further we advocate an upper boundary to prevent the cusum chart rising too high which helps to detect a change back into control we present an algorithm to control the false discovery rate when considering cusum charts based on multiple streams of data we consider two definitions of a false discovery signalling out of control when the observations have been in control since the start and signalling out of control when the observations have been in control since the last time the chart was at zero we prove that the false discovery rate is controlled under both these definitions simultaneously simulations reveal the difference in false discovery rate control when using these and other desirable definitions of a false discovery copyright 2013 oxford university press

information geometric approach to inferring causal directions while conventional approaches to causal inference are mainly based on conditional in dependences recent methods also account for the shape of conditional distributions the idea is that the causal hypothesis x causes y imposes that the marginal distribution p x and the conditional distribution p y x represent independent mechanisms of nature recently it has been postulated that the shortest description of the joint distribution p x y should therefore be given by separate descriptions of p x and p y x since description length in the sense of kolmogorov complexity is uncomputable practical implementations rely on other notions of independence here we define independence via orthogonality in information space this way we can explicitly describe the kind of dependence that occurs between p y and p x y making the causal hypothesis y causes x implausible remarkably this asymmetry between cause and effect becomes particularly simple if x and y are deterministically related we present an inference method that works in this case we also discuss some theoretical results for the non deterministic case although it is not clear how to employ them for a more general inference method

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

online rules for control of false discovery rate and false discovery exceedance multiple hypothesis testing is a core problem in statistical inference and arises in almost every scientific field given a set of null hypotheses mathcal h n h 1 ldots h n benjamini and hochberg j r stat soc ser b stat methodol 57 1995 289 300 introduced the false discovery rate mathrm fdr which is the expected proportion of false positives among rejected null hypotheses and proposed a testing procedure that controls mathrm fdr below a pre assigned significance level nowadays mathrm fdr is the criterion of choice for large scale multiple hypothesis testing in this paper we consider the problem of controlling mathrm fdr in an online manner concretely we consider an ordered possibly infinite sequence of null hypotheses mathcal h h 1 h 2 h 3 ldots where at each step i the statistician must decide whether to reject hypothesis h i having access only to the previous decisions this model was introduced by foster and stine j r stat soc ser b stat methodol 70 2008 429 444 we study a class of generalized alpha investing procedures first introduced by aharoni and rosset j r stat soc ser b stat methodol 76 2014 771 794 we prove that any rule in this class controls online mathrm fdr provided p values corresponding to true nulls are independent from the other p values earlier work only established mathrm mfdr control next we obtain conditions under which generalized alpha investing controls mathrm fdr in the presence of general p values dependencies we also develop a modified set of procedures that allow to control the false discovery exceedance the tail of the proportion of false discoveries finally we evaluate the performance of online procedures on both synthetic and real data comparing them with offline approaches such as adaptive benjamini hochberg

the relationship between breaking the diffie hellman protocol and computing discrete logarithms both uniform and nonuniform results concerning the security of the diffie hellman key exchange protocol are proved first it is shown that in a cyclic group g of order g prod p i e i where all the multiple prime factors of g are polynomial in log g there exists an algorithm that reduces the computation of discrete logarithms in g to breaking the diffie hellman protocol in g and has complexity sqrt max nu p i cdot log g o 1 where nu p stands for the minimum of the set of largest prime factors of all the numbers d in the interval p 2 sqrt p 1 p 2 sqrt p 1 under the unproven but plausible assumption that nu p is polynomial in log p this reduction implies that the diffie hellman problem and the discrete logarithm problem are polynomial time equivalent in g second it is proved that the diffie hellman problem and the discrete logarithm problem are equivalent in a uniform sense for groups whose orders belong to certain classes there exists a polynomial time reduction algorithm that works for all those groups moreover it is shown that breaking the diffie hellman protocol for a small but nonnegligible fraction of the instances is equally difficult as breaking it for all instances finally efficient constructions of groups are described for which the algorithm reducing the discrete logarithm problem to the diffie hellman problem is efficiently constructible

exact calculations for false discovery proportion with application to least favorable configurations in a context of multiple hypothesis testing we provide several new exact calculations related to the false discovery proportion fdp of step up and step down procedures for step up procedures we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable which leads to explicit computations of the c d f the s th moment and the mean of the fdp the latter corresponding to the false discovery rate fdr for step down procedures we derive what is to our knowledge the first explicit formula for the fdr valid for any alternative c d f of the p values we also derive explicit computations of the power for both step up and step down procedures these formulas are explicit in the sense that they only involve the parameters of the model and the c d f of the order statistics of i i d uniform variables the p values are assumed either independent or coming from an equicorrelated multivariate normal model and an additional mixture model for the true false hypotheses is used this new approach is used to investigate new results which are of interest in their own right related to least most favorable configurations for the fdr and the variance of the fdp

on a generalized false discovery rate the concept of k fwer has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least k false rejections for some flxed k 1 a less conservative notion the k fdr has been introduced very recently by sarkar 19 generalizing the false discovery rate of banjamini and hochberg 1 in this article we bring newer insight to the k fdr considering a mixture model involving independent p values before motivating the developments of some new procedures that control it we prove the k fdr control of the proposed methods under a slightly weaker condition than in the mixture model we provide numerical evidence of the proposed methods superior power performance over some kfwer and k fdr methods finally we apply our methods to a real data set

total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities total positivity properties of multivariate densities are useful in deducing positive dependence of random vector components and related probability inequalities in this paper we determine necessary and sufficient conditions for total positivity of absolute value multinormal variables the results are applied to obtain positive dependence and associated inequalities for the multinormal and related distributions e g the multivariate t and wishart distributions inequalities of this type yield bounds for multivariate confidence set probabilities

multiple testing via fdrl for large scale imaging data the multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data typically the spatial signals are sparse but clustered this paper provides empirical evidence that for a range of commonly used control levels the conventional fdr procedure can lack the ability to detect statistical significance even if the p values under the true null hypotheses are independent and uniformly distributed more generally ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the fdr procedure this paper first introduces a scalar quantity to characterize the extent to which the lack of identification phenomenon lip of the fdr procedure occurs second we propose a new multiple comparison procedure called fdrl to accommodate the spatial information of neighboring p values via a local aggregation of p values theoretical properties of the fdrl procedure are investigated under weak dependence of p values it is shown that the fdrl procedure alleviates the lip of the fdr procedure thus substantially facilitating the selection of more stringent control levels simulation evaluations indicate that the fdrl procedure improves the detection sensitivity of the fdr procedure with little loss in detection specificity the computational simplicity and detection effectiveness of the fdrl procedure are illustrated through a real brain fmri dataset

stepup procedures controlling generalized fwer and generalized fdr in many applications of multiple hypothesis testing where more than one false rejection can be tolerated procedures controlling error rates measuring at least k false rejections instead of at least one for some fixed k 1 can potentially increase the ability of a procedure to detect false null hypotheses the k fwer a generalized version of the usual familywise error rate fwer is such an error rate that has recently been introduced in the literature and procedures controlling it have been proposed a further generalization of a result on the k fwer is provided in this article in addition an alternative and less conservative notion of error rate the k fdr is introduced in the same spirit as the k fwer by generalizing the usual false discovery rate fdr a k fwer procedure is constructed given any set of increasing constants by utilizing the kth order joint null distributions of the p values without assuming any specific form of dependence among all the p values procedures controlling the k fdr are also developed by using the kth order joint null distributions of the p values first assuming that the sets of null and nonnull p values are mutually independent or they are jointly positively dependent in the sense of being multivariate totally positive of order two mtp2 and then discarding that assumption about the overall dependence among the p values

sequential selection procedures and false discovery rate control summary we consider a multiple hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block of hypotheses a rejection rule in this setting amounts to a procedure for choosing the stopping point k this setting is inspired by the sequential nature of many model selection problems where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter we propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting we also show how the methods can be applied to model selection by using recent results on p values in sequential model selection settings

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

a digital signature scheme secure against adaptive chosen message attacks we present a digital signature scheme based on the computational difficulty of integer factorization the scheme possesses the novel property of being robust against an adaptive chosen message attack an adversary who receives signatures for messages of his choice where each message may be chosen in a way that depends on the signatures of previously chosen messages cannot later forge the signature of even a single additional message this may be somewhat surprising since in the folklore the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosen message attack were considered to be contradictory more generally we show how to construct a signature scheme with such properties based on the existence of a claw free pair of permutations a potentially weaker assumption than the intractibility of integer factorization the new scheme is potentially practical signing and verifying signatures are reasonably fast and signatures are compact

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

wavelet thresholding with bayesian false discovery rate control la procedure du false discovery rate fdr est aujourd hui une methode largement repandue pour gerer les questions de multiplicite liees a des donnees multidimensionnelles la definition du fdr trouveune interpretation naturelle dans le cadre bayesien a savoir la proportion attendue d hypotheses nulles rejetees a tort a seuil de significativite donne dans cet article nous proposons de controler le fdr positif par une approche bayesienne dont la regle de rejet est basee sur les probabilites posterieures des hypotheses nulles le lien entre les degres de significativite bayesiens et frequentistes a ete etudie dans plusieurs contextes ici nous elargissons la comparaison aux tests multiples avec controle du fdr et illustrons la procedure par une application au seuillage en ondelettes le probleme consiste a recuperer un signal a partir de mesures bruitees ceci implique d extraire des coefficients d ondelettes resultant du vrai signal et peut etre formule comme un probleme de test d hypotheses multiples nous utilisons des exemples simules pour comparer les performances de notre approche a la procedure de benjamini et hochberg 1995 nous illustrons egalement cette methode au moyen de donnees issues de l analyse spectrale par resonance magnetique nucleaire du cerveau humain

local causal and markov blanket induction for causal discovery and feature selection for classification part ii analysis and extensions in part i of this work we introduced and evaluated the generalized local learning gll framework for producing local causal and markov blanket induction algorithms in the present second part we analyze the behavior of gll algorithms and provide extensions to the core methods specifically we investigate the empirical convergence of gll to the true local neighborhood as a function of sample size moreover we study how predictivity improves with increasing sample size then we investigate how sensitive are the algorithms to multiple statistical testing especially in the presence of many irrelevant features next we discuss the role of the algorithm parameters and also show that markov blanket and causal graph concepts can be used to understand deviations from optimality of state of the art non causal algorithms the present paper also introduces the following extensions to the core gll framework parallel and distributed versions of gll algorithms versions with false discovery rate control strategies for constructing novel heuristics for specific domains and divide and conquer local to global learning lgl strategies we test the generality of the lgl approach by deriving a novel lgl based algorithm that compares favorably to the state of the art global learning algorithms in addition we investigate the use of non causal feature selection methods to facilitate global learning open problems and future research paths related to local and local to global causal learning are discussed

correlated z values and the accuracy of large scale statistical estimates we consider large scale studies in which there are hundreds or thousands of correlated cases to investigate each represented by its own normal variate typically a z value a familiar example is provided by a microarray experiment comparing healthy with sick subjects expression levels for thousands of genes this paper concerns the accuracy of summary statistics for the collection of normal variates such as their empirical cdf or a false discovery rate statistic it seems like we must estimate an n by n correlation matrix n the number of cases but our main result shows that this is not necessary good accuracy approximations can be based on the root mean square correlation over all n n 1 2 pairs a quantity often easily estimated a second result shows that z values closely follow normal distributions even under nonnull conditions supporting application of the main theorem practical application of the theory is illustrated for a large leukemia microarray study

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

fiber density estimation from single q shell diffusion imaging by tensor divergence diffusion weighted magnetic resonance imaging provides information about the nerve fiber bundle geometry of the human brain while the inference of the underlying fiber bundle orientation only requires single q shell measurements the absolute determination of their volume fractions is much more challenging with respect to measurement techniques and analysis unfortunately the usually employed multi compartment models cannot be applied to single q shell measurements because the compartment s diffusivities cannot be resolved this work proposes an equation for fiber orientation densities that can infer the absolute fraction up to a global factor this equation which is inspired by the classical mass preservation law in fluid dynamics expresses the fiber conservation associated with the assumption that fibers do not terminate in white matter simulations on synthetic phantoms show that the approach is able to derive the densities correctly for various configurations experiments with a pseudo ground truth phantom show that even for complex brain like geometries the method is able to infer the densities correctly in vivo results with 81 healthy volunteers are plausible and consistent a group analysis with respect to age and gender show significant differences such that the proposed maps can be used as a quantitative measure for group and longitudinal analysis

perturbed phase space dynamics of hard disk fluids abstract the lyapunov spectrum describes the exponential growth or decay of infinitesimal phase space perturbations the perturbation associated with the maximum lyapunov exponent is strongly localized in space and only a small fraction of all particles contributes to the perturbation growth at any instant of time this fraction converges to zero in the thermodynamic large particle number limit for hard disk and hard sphere systems the perturbations belonging to the smallest of the non vanishing exponents are coherently spread out and form orthogonal periodic structures in space the lyapunov modes there are two types of mode polarizations transverse and longitudinal the transverse modes do not propagate but the longitudinal modes do with a speed about one third of the sound speed we characterize the symmetry and the degeneracy of the modes in the thermodynamic limit the lyapunov spectrum has a diverging slope near the intersection with the abscissa no positive lower bound exists for the positive exponents the mode amplitude scales with the inverse square root of the particle number as expected from the normalization of the perturbation vectors

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

active learning of causal networks with intervention experiments and optimal designs the causal discovery from data is important for various scientific investigations because we cannot distinguish the different directed acyclic graphs dags in a markov equivalence class learned from observational data we have to collect further information on causal structures from experiments with external interventions in this paper we propose an active learning approach for discovering causal structures in which we first find a markov equivalence class from observational data and then we orient undirected edges in every chain component via intervention experiments separately in the experiments some variables are manipulated through external interventions we discuss two kinds of intervention experiments randomized experiment and quasi experiment furthermore we give two optimal designs of experiments a batch intervention design and a sequential intervention design to minimize the number of manipulated variables and the set of candidate structures based on the minimax and the maximum entropy criteria we show theoretically that structural learning can be done locally in subgraphs of chain components without need of checking illegal v structures and cycles in the whole network and that a markov equivalence subclass obtained after each intervention can still be depicted as a chain graph

lyapunov instability of rough hard disk fluids the dynamical instability of rough hard disk fluids in two dimensions is characterized through the lyapunov spectrum and the kolmogorov sinai entropy h ks for a wide range of densities and moments of inertia i for small i the spectrum separates into translation dominated and rotation dominated parts with increasing i the rotation dominated part is gradually filled in at the expense of translation until such a separation becomes meaningless at any density the rate of phase space mixing given by h ks becomes less and less effective the more the rotation affects the dynamics however the degree of dynamical chaos measured by the maximum lyapunov exponent is only enhanced by the rotational degrees of freedom for high density gases but is diminished for lower densities surprisingly no traces of lyapunov modes were found in the spectrum for larger moments of inertia the spatial localization of the perturbation vector associated with the maximum exponent however persists for any i

denoising functional mr images a comparison of wavelet denoising and gaussian smoothing we present a general wavelet based denoising scheme for functional magnetic resonance imaging fmri data and compare it to gaussian smoothing the traditional denoising method used in fmri analysis one dimensional wavelab thresholding routines were adapted to two dimensional 2 d images and applied to 2 d wavelet coefficients to test the effect of these methods on the signal to noise ratio snr we compared the snr of 2 d fmri images before and after denoising using both gaussian smoothing and wavelet based methods we simulated a fmri series with a time signal in an active spot and tested the methods on noisy copies of it the denoising methods were evaluated in two ways by the average temporal snr inside the original activated spot and by the shape of the spot detected by thresholding the temporal snr maps denoising methods that introduce much smoothness are better suited for low snrs but for images of reasonable quality they are not preferable because they introduce heavy deformations wavelet based denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions we also performed statistical parametric mapping on the denoised simulated time series as well as on a real fmri data set false discovery rate control was used to correct for multiple comparisons the results show that the methods that produce smooth images introduce more false positives the less smoothing wavelet based methods although generating more false negatives produce a smaller total number of errors than gaussian smoothing or wavelet based methods with a large smoothing effect

dependency and false discovery rate asymptotics some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step up procedure lsu for testing n hypotheses when test statistics are dependent in this paper we investigate the expected error rate eer and the false discovery rate fdr in some extreme parameter configurations when n tends to infinity for test statistics being exchangeable under null hypotheses all results are derived in terms of p values in a general setup we present a series of results concerning the interrelation of simes rejection curve and the limiting empirical distribution function of the p values main objects under investigation are largest limiting crossing points between these functions which play a key role in deriving explicit formulas for eer and fdr as specific examples we investigate equi correlated normal and t variables in more detail and compute the limiting eer and fdr theoretically and numerically a surprising limit behavior occurs if these models tend to independence

multiple tests based on a gaussian approximation of the unitary events method with delayed coincidence count the unitary events ue method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons the detection of coincidences is usually based on binned coincidence count grun 1996 which is known to be subject to loss in synchrony detection grun diesmann grammont riehle aertsen 1999 this defect has been corrected by the multiple shift coincidence count grun et al 1999 the statistical properties of this count have not been further investigated until this work the formula being more difficult to deal with than the original binned count first we propose a new notion of coincidence count the delayed coincidence count which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains moreover it generalizes this notion to nondiscretized point processes allowing us to propose a new gaussian approximation of the count since unknown parameters are involved in the approximation we perform a plug in step where unknown parameters are replaced by estimated ones leading to a modification of the approximating distribution finally the method takes the multiplicity of the tests into account via a benjamini and hochberg approach benjamini hochberg 1995 to guarantee a prescribed control of the false discovery rate we compare our new method mtgaue multiple tests based on a gaussian approximation of the unitary events and the ue method proposed in grun et al 1999 over various simulations showing that mtgaue extends the validity of the previous method in particular mtgaue is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model furthermore mtgaue is applied on real data

optimal structure identification with greedy search in this paper we prove the so called meek conjecture in particular we show that if a dag h is an independence map of another dag g then there exists a finite sequence of edge additions and covered edge reversals in g such that 1 after each edge modification h remains an independence map of g and 2 after all modifications g h as shown by meek 1997 this result has an important consequence for bayesian approaches to learning bayesian networks from data in the limit of large sample size there exists a two phase greedy search algorithm that when applied to a particular sparsely connected search space provably identifies a perfect map of the generative distribution if that perfect map is a dag we provide a new implementation of the search space using equivalence classes as states for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain finally using both synthetic and real world datasets we demonstrate that the two phase greedy approach leads to good solutions when learning with finite sample sizes

proportion of non zero normal means universal oracle equivalences and uniformly consistent estimators d0 we propose a general approach to construct the universal oracle equivalence of the proportion the construction is based on the underlying characteristic function the oracle equivalence reduces the problem of estimating the proportion to the problem of estimating the oracle which is relatively easier to handle in fact the oracle equivalence naturally yields a family of estimators for the proportion which are consistent under mild conditions uniformly across a wide class of parameters the approach compares favourably with recent works by meinshausen and rice and genovese and wasserman in particular the consistency is proved for an unprecedentedly broad class of situations the class is almost the largest that can be hoped for without further constraints on the model we also discuss various extensions of the approach report results on simulation experiments and make connections between the approach and several recent procedures in large scale multiple testing including the false discovery rate approach and the local false discovery rate approach

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

detecting differentially expressed genes in microarrays using bayesian model selection dna microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease the high throughput nature of these arrays where differential expression for thousands of genes can be measured simultaneously creates an enormous wealth of information but also poses a challenge for data analysis because of the large multiple testing problem involved the solution has generally been to focus on optimizing false discovery rates while sacrificing power the drawback of this approach is that more subtle expression differences will be missed that might give investigators more insight into the genetic environment necessary for a disease process to take hold we introduce a new method for detecting differentially expressed genes based on a high dimensional model selection technique bayesian anova for microarrays bam which strikes a balance between false rejections and false nonrejections the basis of the new approach involves a weighted average of generalized ridge

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

on false discovery control under dependence a popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent this paper generalizes the random effects model to a conditional dependence model which allows dependence between null hypotheses the dependence can be useful to characterize the spatial structure of the null hypotheses asymptotic properties of false discovery proportions and numbers of rejected hypotheses are explored and a large sample distributional theory is obtained

familywise robustness criteria for multiple comparison procedures a criticism of multiple comparison procedures is that the family of inferences over which an error rate is controlled is often arbitrarily selected yet the conclusion may depend heavily on the choice of the family such ambiguity is most likely in large exploratory studies requiring numerous simultaneous inferences in ambiguous situations it is desirable that results of multiple comparison procedures depend little on the chosen family to assess this we propose several familywise robustness criteria to evaluate such procedures and we find some of their properties theoretically and by simulation procedures that control the false discovery rate seem to be familywise robust

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

selective inference on multiple families of hypotheses summary in many complex multiple testing problems the hypotheses are divided into families given the data families with evidence for true discoveries are selected and hypotheses within them are tested neither controlling the error rate in each family separately nor controlling the error rate over all hypotheses together can assure some level of confidence about the filtration of errors within the selected families we formulate this concern about selective inference in its generality for a very wide class of error rates and for any selection criterion and present an adjustment of the testing level inside the selected families that retains control of the expected average error over the selected families

α investing a procedure for sequential control of expected false discoveries summary investing is an adaptive sequential methodology that encompasses a large family of procedures for testing multiple hypotheses all control mfdr which is the ratio of the expected number of false rejections to the expected number of rejections mfdr is a weaker criterion than the false discovery rate which is the expected value of the ratio we compensate for this weakness by showing that investing controls mfdr at every rejected hypothesis investing resembles spending that is used in sequential trials but it has a key difference when a test rejects a null hypothesis investing earns additional probability towards subsequent tests investing hence allows us to incorporate domain knowledge into the testing procedure and to improve the power of the tests in this way investing enables the statistician to design a testing procedure for a specific problem while guaranteeing control of mfdr

efficient generic on line off line threshold signatures without key exposure the hash sign switch paradigm was firstly proposed by shamir and tauman with the aim to design an efficient on line off line signature scheme nonetheless all existing on line off line signature schemes based on this paradigm suffer from the key exposure problem of chameleon hashing to avoid this problem the signer should pre compute and store a plenty of different chameleon hash values and the corresponding signatures on the hash values in the off line phase and send the collision and the signature for a certain hash value in the on line phase hence the computation and storage cost for the off line phase and the communication cost for the on line phase in shamir tauman s signature scheme are still a little more overload in this paper we first introduce a special double trapdoor hash family based on the discrete logarithm assumption and then incorporate it to construct a more efficient generic on line off line signature scheme without key exposure furthermore we also present the first key exposure free generic on line off line threshold signature scheme without a trusted dealer additionally we prove that the proposed schemes have achieved the desired security requirements

support vector machines for dyadic data we describe a new technique for the analysis of dyadic data where two sets of objects row and column objects are characterized by a matrix of numerical values that describe their mutual relationships the new technique called potential support vector machine p svm is a large margin method for the construction of classifiers and regression functions for the column objects contrary to standard support vector machine approaches the p svm minimizes a scale invariant capacity measure and requires a new set of constraints as a result the p svm method leads to a usually sparse expansion of the classification and regression functions in terms of the row rather than the column objects and can handle data and kernel matrices that are neither positive definite nor square we then describe two complementary regularization schemes the first scheme improves generalization performance for classification and regression tasks the second scheme leads to the selection of a small informative set of row support objects and can be applied to feature selection benchmarks for classification regression and feature selection tasks are performed with toy data as well as with several real world data sets the results show that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as true dyadic data sets in addition a theoretical justification is provided for the new approach

joint mean and covariance estimation with unreplicated matrix variate data abstractit has been proposed that complex populations such as those that arise in genomics studies may exhibit dependencies among observations as well as among variables this gives rise to the challenging problem of analyzing unreplicated high dimensional data with unknown mean and dependence structures matrix variate approaches that impose various forms of inverse covariance sparsity allow flexible dependence structures to be estimated but cannot directly be applied when the mean and covariance matrices are estimated jointly we present a practical method utilizing generalized least squares and penalized inverse covariance estimation to address this challenge we establish consistency and obtain rates of convergence for estimating the mean parameters and covariance matrices the advantages of our approaches are i dependence graphs and covariance structures can be estimated in the presence of unknown mean structure ii the mean structure becomes more efficiently estimated when accounting for

a linear non gaussian acyclic model for causal discovery in recent years several methods have been proposed for the discovery of causal structure from non experimental data such methods make various assumptions on the data generating process to facilitate its identification from purely observational data continuing this line of research we show how to discover the complete causal structure of continuous valued data under the assumptions that a the data generating process is linear b there are no unobserved confounders and c disturbance variables have non gaussian distributions of non zero variances the solution relies on the use of the statistical method known as independent component analysis and does not require any pre specified time ordering of the variables we provide a complete matlab package for performing this lingam analysis short for linear non gaussian acyclic model and demonstrate the effectiveness of the method using artificially generated data and real world data

accumulation tests for fdr control in ordered hypothesis testing abstractmultiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses with relatively few true signals in this article we consider the multiple testing problem where prior information is available for instance from an earlier study under different experimental conditions that can allow us to test the hypotheses as a ranked list to increase the number of discoveries given an ordered list of n hypotheses the aim is to select a data dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate fdr generalizing several existing methods we develop a family of accumulation tests to choose a cutoff k that adapts to the amount of signal at the top of the ranked list we introduce a new method in this family the hingeexp method which offers higher power to detect true signals compared to existing techniques our theoretical results prove that these metho

chip chip data model and analysis summary chip chip or chip on chip is a technology for isolation and identification of genomic sites occupied by specific dna binding proteins in living cells the chip chip signals can be obtained over the whole genome by tiling arrays where a peak shape is generally observed around a protein binding site in this article we describe the chip chip process and present a probability model for chip chip data we then propose a model based method for recognizing the peak shapes for the purpose of detecting protein binding sites we also investigate the issue of bandwidth in nonparametric kernel smoothing method

estimating the false discovery rate using the stochastic approximation algorithm testing of multiple hypotheses involves statistics that are strongly dependent in some applications but most work on this subject is based on the assumption of independence we propose a new method for estimating the false discovery rate of multiple hypothesis tests in which the density of test scores is estimated parametrically by minimizing the kullback leibler distance between the unknown density and its estimator using the stochastic approximation algorithm and the false discovery rate is estimated using the ensemble averaging method our method is applicable under general dependence between test statistics numerical comparisons between our method and several competitors conducted on simulated and real data examples show that our method achieves more accurate control of the false discovery rate in almost all scenarios

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

local causal and markov blanket induction for causal discovery and feature selection for classification part i algorithms and empirical evaluation we present an algorithmic framework for learning local causal structure around target variables of interest in the form of direct causes effects and markov blankets applicable to very large data sets with relatively small samples the selected feature sets can be used for causal discovery and classification the framework generalized local learning or gll can be instantiated in numerous ways giving rise to both existing state of the art as well as novel algorithms the resulting algorithms are sound under well defined sufficient conditions in a first set of experiments we evaluate several algorithms derived from this framework in terms of predictivity and feature set parsimony and compare to other local causal discovery methods and to state of the art non causal feature selection methods using real data a second set of experimental evaluations compares the algorithms in terms of ability to induce local causal neighborhoods using simulated and resimulated data and examines the relation of predictivity with causal induction performance our experiments demonstrate consistently with causal feature selection theory that local causal feature selection methods under broad assumptions encompassing appropriate family of distributions types of classifiers and loss functions exhibit strong feature set parsimony high predictivity and local causal interpretability although non causal feature selection methods are often used in practice to shed light on causal relationships we find that they cannot be interpreted causally even when they achieve excellent predictivity therefore we conclude that only local causal techniques should be used when insight into causal structure is sought in a companion paper we examine in depth the behavior of gll algorithms provide extensions and show how local techniques can be used for scalable and accurate global causal graph learning

false discovery control with p value weighting we present a method for multiple hypothesis testing that maintains control of the false discovery rate while incorporating prior information about the hypotheses the prior information takes the form of p value weights if the assignment of weights is positively associated with the null hypotheses being false the procedure improves power except in cases where power is already near one even if the assignment of weights is poor power is only reduced slightly as long as the weights are not too large we also provide a similar method to control false discovery exceedance

characterization of bayes procedures for multiple endpoint problems and inadmissibility of the step up procedure the problem of multiple endpoint testing for k endpoints is treated as a 2 k finite action problem the loss function chosen is a vector loss function consisting of two components the two components lead to a vector risk one component of the vector risk is the false rejection rate frr that is the expected number of false rejections the other component is the false acceptance rate far that is the expected number of acceptances for which the corresponding null hypothesis is false this loss function is more stringent than the positive linear combination loss function of lehmann ann math statist 28 1957 1 25 and cohen and sackrowitz ann statist 2005 33 126 144 in the sense that the class of admissible rules is larger for this vector risk formulation than for the linear combination risk function in other words fewer procedures are inadmissible for the vector risk formulation the statistical model assumed is that the vector of variables z is multivariate normal with mean vector and known intraclass covariance matrix e the endpoint hypotheses are h i i 0 vs k i i 0 1 k a characterization of all symmetric bayes procedures and their limits is obtained the characterization leads to a complete class theorem the complete class theorem is used to provide a useful necessary condition for admissibility of a procedure the main result is that the step up multiple endpoint procedure is shown to be inadmissible

outlier detection and false discovery rates for whole genome dna matching we define a statistic called the matching statistic for locating regions of the genome that exhibit excess similarity among cases when compared to controls such regions are reasonable candidates for harboring disease genes we find the asymptotic distribution of the statistic while accounting for correlations among sampled individuals we then use the benjamini and hochberg false discovery rate fdr method for multiple hypothesis testing to find regions of excess sharing the p values for each region involve estimated nuisance parameters under appropriate conditions we show that the fdr method based on p values and with estimated nuisance parameters asymptotically preserves the fdr property finally we apply the method to a pilot study on schizophrenia

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

sensitivity analysis for the cross match test with applications in genomics the cross match test is an exact distribution free test of no treatment effect on a high dimensional outcome in a randomized experiment the test uses optimal nonbipartite matching to pair 2i subjects into i pairs based on similar outcomes and the cross match statistic a is the number of times that a treated subject was paired with a control rejecting for small values of a if the test is applied in an observational study in which treatments are not randomly assigned then it may be comparing treated and control subjects who are not comparable and thus may falsely reject a true null hypothesis of no treatment effect we develop a sensitivity analysis for the cross match test and apply it in an observational study of the effects of smoking on gene expression levels in addition we develop a sensitivity analysis for several multiple testing procedures using the cross match test and apply it to 1627 molecular function categories in gene ontology

panning for gold model x knockoffs for high dimensional controlled variable selection many contemporary large scale applications involve building interpretable models linking a large set of potential covariates to a response in a non linear fashion such as when the response is binary although this modelling problem has been extensively studied it remains unclear how to control the fraction of false discoveries effectively even in high dimensional logistic regression not to mention general high dimensional non linear models to address such a practical problem we propose a new framework of model x knockoffs which reads from a different perspective the knockoff procedure that was originally designed for controlling the false discovery rate in linear models whereas the knockoffs procedure is constrained to homoscedastic linear models with n p the key innovation here is that model x knockoffs provide valid inference from finite samples in settings in which the conditional distribution of the response is arbitrary and completely unknown furthermore this holds no matter the number of covariates correct inference in such a broad setting is achieved by constructing knockoff variables probabilistically instead of geometrically to do this our approach requires that the covariates are random independent and identically distributed rows with a distribution that is known although we provide preliminary experimental evidence that our procedure is robust to unknown or estimated distributions to our knowledge no other procedure solves the controlled variable selection problem in such generality but in the restricted settings where competitors exist we demonstrate the superior power of knockoffs through simulations finally we apply our procedure to data from a case control study of crohn s disease in the uk making twice as many discoveries as the original analysis of the same data