causal inference through a witness protection program one of the most fundamental problems in causal inference is the estimation of a causal effect when treatment and outcome are confounded this is difficult in an observational study because one has no direct evidence that all confounders have been adjusted for we introduce a novel approach for estimating causal effects that exploits observational conditional independencies to suggest weak paths in an unknown causal graph the widely used faithfulness condition of spirtes et al is relaxed to allow for varying degrees of path cancellations that imply conditional independencies but do not rule out the existence of confounding causal paths the output is a posterior distribution over bounds on the average causal effect via a linear programming approach and bayesian inference we claim this approach should be used in regular practice as a complement to other tools in observational studies

matchgate and space bounded quantum computations are equivalent matchgates are an especially multiflorous class of two qubit nearest neighbour quantum gates defined by a set of algebraic constraints they occur for example in the theory of perfect matchings of graphs non interacting fermions and one dimensional spin chains we show that the computational power of circuits of matchgates is equivalent to that of space bounded quantum computation with unitary gates with space restricted to being logarithmic in the width of the matchgate circuit in particular for the conventional setting of polynomial sized logarithmic space generated families of matchgate circuits known to be classically simulatable we characterize their power as coinciding with polynomial time and logarithmic space bounded universal unitary quantum computation

estimation of directed acyclic graphs through two stage adaptive lasso for gene network inference abstractgraphical models are a popular approach to find dependence and conditional independence relationships between gene expressions directed acyclic graphs dags are a special class of directed graphical models where all the edges are directed edges and contain no directed cycles the dags are well known models for discovering causal relationships between genes in gene regulatory networks however estimating dags without assuming known ordering is challenging due to high dimensionality the acyclic constraints and the presence of equivalence class from observational data to overcome these challenges we propose a two stage adaptive lasso approach called ns dist which performs neighborhood selection ns in stage 1 and then estimates dags by the discrete improving search with tabu dist algorithm within the selected neighborhood simulation studies are presented to demonstrate the effectiveness of the method and its computational efficiency two real data examples are used to demonstrate the p

complete identification methods for the causal hierarchy we consider a hierarchy of queries about causal relationships in graphical models where each level in the hierarchy requires more detailed information than the one below the hierarchy consists of three levels associative relationships derived from a joint distribution over the observable variables cause effect relationships derived from distributions resulting from external interventions and counterfactuals derived from distributions that span multiple parallel worlds and resulting from simultaneous possibly conflicting observations and interventions we completely characterize cases where a given causal query can be computed from information lower in the hierarchy and provide algorithms that accomplish this computation specifically we show when effects of interventions can be computed from observational studies and when probabilities of counterfactuals can be computed from experimental studies we also provide a graphical characterization of those queries which cannot be computed by any method from queries at a lower layer of the hierarchy

causal inference in paired two arm experimental studies under noncompliance with application to prognosis of myocardial infarction motivated by a study about prompt coronary angiography in myocardial infarction we propose a method to estimate the causal effect of a treatment in two arm experimental studies with possible noncompliance in both treatment and control arms we base the method on a causal model for repeated binary outcomes before and after the treatment which includes individual covariates and latent variables for the unobserved heterogeneity between subjects moreover given the type of noncompliance the model assumes the existence of three subpopulations of subjects compliers never takers and always takers we estimate the model using a two step estimator at the first step we estimate the probability that a subject belongs to one of the three subpopulations on the basis of the available covariates at the second step we estimate the causal effects through a conditional logistic method the implementation of which depends on the results from the first step the estimator is approximately consistent and under certain circumstances exactly consistent we provide evidence that the bias is negligible in relevant situations we compute standard errors on the basis of a sandwich formula the application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next 2 years with a log odds of about 2 given that noncompliance is significant for patients being given the treatment because of high risk conditions classical estimators fail to detect or at least underestimate this effect copyright 2013 john wiley sons ltd

chain graph models and their causal interpretations chain graphs are a natural generalization of directed acyclic graphs and undirected graphs however the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent there are many simple and apparently plausible but ultimately fallacious interpretations of chain graphs that are often invoked implicitly or explicitly these interpretations also lead to flawed methods for applying background knowledge to model selection we present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from the equilibrium distributions of dynamic models with feed back these dynamic interpretations lead to a simple theory of intervention extending the theory developed for directed acyclic graphs finally we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feed back in econometrics

causal diagrams for empirical research summary the primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject matter information in particular the paper develops a principled nonparametric framework for causal inference in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data if so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions otherwise the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained

estimating high dimensional directed acyclic graphs with the pc algorithm we consider the pc algorithm spirtes et al 2000 for estimating the skeleton and equivalence class of a very high dimensional directed acyclic graph dag with corresponding gaussian distribution the pc algorithm is computationally feasible and often very fast for sparse problems with many nodes variables and it has the attractive property to automatically achieve high computational efficiency as a function of sparseness of the true underlying dag we prove uniform consistency of the algorithm for very high dimensional sparse dags where the number of nodes is allowed to quickly grow with sample size n as fast as o na for any 0 a the sparseness assumption is rather minimal requiring only that the neighborhoods in the dag are of lower order than sample size n we also demonstrate the pc algorithm for simulated data

clifford gates in the holant framework abstract we show that the clifford gates and stabilizer circuits in the quantum computing literature which admit efficient classical simulation are equivalent to affine signatures under a unitary condition the latter is a known class of tractable functions under the holant framework

special matchings and kazhdan lusztig polynomials abstract in 1979 kazhdan and lusztig defined for every coxeter group w a family of polynomials indexed by pairs of elements of w which have become known as the kazhdan lusztig polynomials of w and which have proven to be of importance in several areas of mathematics in this paper we show that the combinatorial concept of a special matching plays a fundamental role in the computation of these polynomials our results also imply and generalize the recent one in adv in math 180 2003 146 175 on the combinatorial invariance of kazhdan lusztig polynomials

uniform consistency in causal inference there is a long tradition of representing causal relationships by directed acyclic graphs wright 1934 spirtes 1994 spirtes et al 1993 and pearl verma 1991 describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables and or an unknown time order and that under weak conditions for certain combinations of directed acyclic graphs and probability distributions are asymptotically in sample size consistent these results are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables we resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures we show that the asymptotically consistent procedures are pointwise consistent but uniformly consistent tests do not exist thus no finite sample size can ever be guaranteed to approximate the asymptotic results we also show the nonexistence of valid consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators our results make no assumption about the form of the tests or estimators in particular the tests could be classical independence tests they could be bayes tests or they could be tests based on scoring methods such as bic or aic the implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper the results hinge on the following fact it is possible to find for each sample size n distributions p and q such that p and q are empirically indistinguishable and yet p and q correspond to different causal effects

bounds on treatment effects from studies with imperfect compliance abstract this article establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect the bounds provided are the tightest possible given the distribution of assignments treatments and responses the formulas show that even with high rates of noncompliance experimental data can yield useful and sometimes accurate information on the average effect of a treatment on the population

effect analysis and causation in linear structural equation models this paper considers total and direct effects in linear structural equation models adopting a causal perspective that is implicit in much of the literature on the subject the paper concludes that in many instances the effects do not admit the interpretations imparted in the literature drawing a distinction between concomitants and factors the paper concludes that a concomitant has neither total nor direct effects on other variables when a variable is a factor and one or more intervening variables are concomitants the notion of a direct effect is not causally meaningful even when the notion of a direct effect is meaningful the usual estimate of this quantity may be inappropriate the total effect is usually interpreted as an equilibrium multiplier in the case where there are simultaneity relations among the dependent variables in tghe model the results in the literature for the total effects of dependent variables on other dependent variables are not equilibrium multipliers and thus the usual interpretation is incorrect to remedy some of these deficiencies a new effect the total effect of a factorx on an outcomey holding a set of variablesf constant is defined when defined the total and direct effects are a special case of this new effect and the total effect of a dependent variable on a dependent variable is an equilibrium multiplier

simulating threshold circuits by majority circuits we prove that a single threshold gate with arbitrary weights can be simulated by an explicit polynomial size depth 2 majority circuit in general we show that a polynomial size depth d threshold circuit can be simulated uniformly by a polynomial size majority circuit of depth d 1 goldmann hastad and razborov showed in comput complexity 2 1992 pp 277 300 that a nonuniform simulation exists our construction answers two open questions posed by them we give an explicit construction whereas they use a randomized existence argument and we show that such a simulation is possible even if the depth d grows with the number of variables n their simulation gives polynomial size circuits only when d is constant

identifiability stratification and minimum variance estimation of causal effects the weakest sufficient condition for the identifiability of causal effects is the weakly ignorable treatment assignment which implies that potential responses are independent of treatment assignment in each fine subpopulation stratified by a covariate in this paper we expand the independence that holds in fine subpopulations to the case that the independence may also hold in several coarse subpopulations each of which consists of several fine subpopulations and may have overlaps with other coarse subpopulations we first show that the identifiability of causal effects occurs if and only if the coarse subpopulations partition the whole population we then propose a principle called minimum variance principle which says that the estimator possessing the minimum variance is preferred in dealing with the stratification and the estimation of the causal effects the simulation results with the detail programming and a practical example demonstrate that it is a feasible and reasonable way to achieve our goals

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

learning the structure of linear latent variable models we describe anytime search procedures that 1 find disjoint subsets of recorded variables for which the members of each subset are d separated by a single common unrecorded cause if such exists 2 return information about the causal relations among the latent factors so identified we prove the procedure is point wise consistent assuming a the causal relations can be represented by a directed acyclic graph dag satisfying the markov assumption and the faithfulness assumption b unrecorded variables are not caused by recorded variables and c dependencies are linear we compare the procedure with standard approaches over a variety of simulated structures and sample sizes and illustrate its practical value with brief studies of social science data sets finally we consider generalizations for non linear systems

quantum computational networks the theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines quantum gates are the generalization of classical logic gates a single type of gate the universal quantum gate together with quantum unit wires is adequate for constructing networks with any possible quantum computational property

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

on the conditional logistic estimator in two arm experimental studies with non compliance and before after binary outcomes the behavior of the conditional logistic estimator is analyzed under a causal model for two arm experimental studies with possible non compliance in which the effect of the treatment is measured by a binary response variable we show that when non compliance may only be observed in the treatment arm the effect measured on the logit scale of the treatment on compliers and that of the control on non compliers can be identified and consistently estimated under mild conditions the same does not happen for the effect of the control on compliers a simple correction of the conditional logistic estimator is then proposed which allows us to considerably reduce the bias in estimating this quantity and the causal effect of the treatment over control on compliers a two step estimator results on the basis of which we can also set up a wald test for the hypothesis of absence of a causal effect of the treatment the asymptotic properties of the estimator are studied by exploiting the general theory on maximum likelihood estimation of misspecified models finite sample properties of the estimator and of the related wald test are studied by simulation the extension of the approach to the case of missing responses is also outlined the approach is illustrated by an application to a dataset deriving from a study on the efficacy of a training course on the breast self examination practice copyright 2010 john wiley sons ltd

causal reasoning with ancestral graphs causal reasoning is primarily concerned with what would happen to a system under external interventions in particular we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values one prominent approach to tackling this problem is based on causal bayesian networks using directed acyclic graphs as causal diagrams to relate post intervention probabilities to pre intervention probabilities that are estimable from observational data however such causal diagrams are seldom fully testable given observational data in consequence many causal discovery algorithms based on data mining can only output an equivalence class of causal diagrams rather than a single one this paper is concerned with causal reasoning given an equivalence class of causal diagrams represented by a partial ancestral graph we present two main results the first result extends pearl 1995 s celebrated do calculus to the context of ancestral graphs in the second result we focus on a key component of pearl s calculus the property of invariance under interventions and give stronger graphical conditions for this property than those implied by the first result the second result also improves the earlier similar results due to spirtes et al 1993

signed directed acyclic graphs for causal inference formal rules governing signed edges on causal directed acyclic graphs are described in this paper and it is shown how these rules can be useful in reasoning about causality specifically the notions of a monotonic effect a weak monotonic effect and a signed edge are introduced results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables the incorporation of signed edges into the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables it is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data is missing on confounding variables

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

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

computation causation and discovery in science business and policymaking anywhere data are used in prediction two sorts of problems requiring very different methods of analysis often arise the first problems of recognition and classification concerns learning how to use some features of a system to accurately predict other features of that system the second problems of causal discovery concerns learning how to predict those changes to some features of a system that will result if an intervention changes other features this book is about the second more difficult type of problem typical problems of causal discovery are how will a change in commission rates affect the total sales of a company how will a reduction in cigarette smoking among older smokers affect their life expectancy how will a change in the formula a college uses to award scholarships affect its dropout rate these sorts of changes are interventions that directly alter some features of the system and perhaps and this is the question indirectly alter others the contributors discuss recent research and applications using bayes nets or directed graphic representations including representations of feedback of recursive systems the book contains a thorough discussion of foundational issues algorithms proof techniques and applications to economics physics biology educational research and other areas

a general dynamical statistical model with causal interpretation summary we develop a general dynamical model as a framework for causal interpretation we first state a criterion of local independence in terms of measurability of processes that are involved in the doob meyer decomposition of stochastic processes then we define direct and indirect influence we propose a definition of causal influence using the concepts of a physical system this framework makes it possible to link descriptive and explicative statistical models and encompasses quantitative processes and events one of the features of the paper is the clear distinction between the model for the system and the model for the observation we give a dynamical representation of a conventional joint model for human immunodeficiency virus load and cd4 cell counts we show its inadequacy to capture causal influences whereas in contrast known mechanisms of infection by the human immunodeficiency virus can be expressed directly through a system of differential equations

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

a simulation study of finite sample properties of marginal structural cox proportional hazards models motivated by a previously published study of hiv treatment we simulated data subject to time varying confounding affected by prior treatment to examine some finite sample properties of marginal structural cox proportional hazards models we compared a unadjusted b regression adjusted c unstabilized and d stabilized marginal structural inverse probability of treatment ipt weighted model estimators of effect in terms of bias standard error root mean squared error mse and 95 confidence limit coverage over a range of research scenarios including relatively small sample sizes and ten study assessments in the base case scenario resembling the motivating example where the true hazard ratio was 0 5 both ipt weighted analyses were unbiased while crude and adjusted analyses showed substantial bias towards and across the null stabilized ipt weighted analyses remained unbiased across a range of scenarios including relatively small sample size however the standard error was generally smaller in crude and adjusted models in many cases unstabilized weighted analysis showed a substantial increase in standard error compared to other approaches root mse was smallest in the ipt weighted analyses for the base case scenario in situations where time varying confounding affected by prior treatment was absent ipt weighted analyses were less precise and therefore had greater root mse compared with adjusted analyses the 95 confidence limit coverage was close to nominal for all stabilized ipt weighted but poor in crude adjusted and unstabilized ipt weighted analysis under realistic scenarios marginal structural cox proportional hazards models performed according to expectations based on large sample theory and provided accurate estimates of the hazard ratio

introduction to causal inference the goal of many sciences is to understand the mechanisms by which variables came to take on the values they have that is to find a generative model and to predict what the values of those variables would be if the naturally occurring mechanisms were subject to outside manipulations the past 30 years has seen a number of conceptual developments that are partial solutions to the problem of causal inference from observational sample data or a mixture of observational sample and experimental data particularly in the area of graphical causal modeling however in many domains problems such as the large numbers of variables small samples sizes and possible presence of unmeasured causes remain serious impediments to practical applications of these developments the articles in the special topic on causality address these and other problems in applying graphical causal modeling algorithms this introduction to the special topic on causality provides a brief introduction to graphical causal modeling places the articles in a broader context and describes the differences between causal inference and ordinary machine learning classification and prediction problems

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

matchgates and classical simulation of quantum circuits let g a b denote the two qubit gate that acts as the one qubit su 2 gates a and b in the even and odd parity subspaces respectively of two qubits using a clifford algebra formalism we show th

on testing marginal versus conditional independence we consider testing marginal independence versus conditional independence in a trivariate gaussian setting the two models are non nested and their intersection is a union of two marginal independences we consider two sequences of such models one from each type of independence that are closest to each other in the kullback leibler sense as they approach the intersection they become indistinguishable if the signal strength as measured by the product of two correlation parameters decreases faster than the standard parametric rate under local alternatives at such rate we show that the asymptotic distribution of the likelihood ratio depends on where and how the local alternatives approach the intersection to deal with this non uniformity we study a class of envelope distributions by taking pointwise suprema over asymptotic cumulative distribution functions we show that these envelope distributions are well behaved and lead to model selection procedures with rate free uniform error guarantees and near optimal power to control the error even when the two models are indistinguishable rather than insist on a dichotomous choice the proposed procedure will choose either or both models

improving the reliability of causal discovery from small data sets using argumentation we address the problem of improving the reliability of independence based causal discovery algorithms that results from the execution of statistical independence tests on small data sets which typically have low reliability we model the problem as a knowledge base containing a set of independence facts that are related through pearl s well known axioms statistical tests on finite data sets may result in errors in these tests and inconsistencies in the knowledge base we resolve these inconsistencies through the use of an instance of the class of defeasible logics called argumentation augmented with a preference function that is used to reason about and possibly correct errors in these tests this results in a more robust conditional independence test called an argumentative independence test our experimental evaluation shows clear positive improvements in the accuracy of argumentative over purely statistical tests we also demonstrate significant improvements on the accuracy of causal structure discovery from the outcomes of independence tests both on sampled data from randomly generated causal models and on real world data sets

quantum circuits that can be simulated classically in polynomial time a model of quantum computation based on unitary matrix operations was introduced by feynman and deutsch it has been asked whether the power of this model exceeds that of classical turing machines we show here that a significant class of these quantum computations can be simulated classically in polynomial time in particular we show that two bit operations characterized by 4 4 matrices in which the sixteen entries obey a set of five polynomial relations can be composed according to certain rules to yield a class of circuits that can be simulated classically in polynomial time this contrasts with the known universality of two bit operations and demonstrates that efficient quantum computation of restricted classes is reconcilable with the polynomial time turing hypothesis therefore it is possible that the techniques introduced bring the quantum computational model within the realm of algebraic complexity theory in a manner consistent with one view of quantum physics the wave function is simulated deterministically and randomization arises only in the course of making measurements the results generalize the quantum model in that they do not require the matrices to be unitary in a different direction these techniques also yield deterministic polynomial time algorithms for the decision and parity problems for certain classes of read twice boolean formulae all our results are based on the use of gates that are defined in terms of their graph matching properties

causal analysis with chain event graphs as the chain event graph ceg has a topology which represents sets of conditional independence statements it becomes especially useful when problems lie naturally in a discrete asymmetric non product space domain or when much context specific information is present in this paper we show that it can also be a powerful representational tool for a wide variety of causal hypotheses in such domains furthermore we demonstrate that as with causal bayesian networks cbns the identifiability of the effects of causal manipulations when observations of the system are incomplete can be verified simply by reference to the topology of the ceg we close the paper with a proof of a back door theorem for cegs analogous to pearl s back door theorem for cbns

markov properties for linear causal models with correlated errors a linear causal model with correlated errors represented by a dag with bi directed edges can be tested by the set of conditional independence relations implied by the model a global markov property specifies by the d separation criterion the set of all conditional independence relations holding in any model associated with a graph a local markov property specifies a much smaller set of conditional independence relations which will imply all other conditional independence relations which hold under the global markov property for dags with bi directed edges associated with arbitrary probability distributions a local markov property is given in richardson 2003 which may invoke an exponential number of conditional independencies in this paper we show that for a class of linear structural equation models with correlated errors there is a local markov property which will invoke only a linear number of conditional independence relations for general linear models we provide a local markov property that often invokes far fewer conditional independencies than that in richardson 2003 the results have applications in testing linear structural equation models with correlated errors

the hodge theory of soergel bimodules we prove soergel s conjecture on the characters of indecomposable soergel bimodules we deduce that kazhdan lusztig polynomials have positive coecients for arbitrary coxeter systems using results of soergel one may deduce an algebraic proof of the kazhdan lusztig conjecture

the combinatorial invariance conjecture for parabolic kazhdan lusztig polynomials of lower intervals abstract the aim of this work is to prove a conjecture related to the combinatorial invariance conjecture of kazhdan lusztig polynomials in the parabolic setting for lower intervals in every arbitrary coxeter group this result improves and generalizes among other results the main results of brenti et al 2006 6 marietti 2016 21

on the interpretation and observation of laws a law with factors x and concomitants z specifies a distribution given z of a potential value yx that is defined for each x whether or not it is observed an observed distribution of y given x and z agrees with the law if and only if given z the observed x is independent of yx or equivalently of the joint effect of ux of excluded variables on yx to establish such independence in non experimental data requires exhaustive exploration of the effects of concomitants causal and non causal r2 and f are irrelevant we show how the model free theory applies to linear models time series and simultaneous equations and point out its bayesian implications

agnostically learning halfspaces we give a computationally efficient algorithm that learns under distributional assumptions a halfspace in the difficult agnostic framework of kearns schapire and sellie mach learn 17 1994 pp 115 141 where a learner is given access to a distribution on labelled examples but where the labelling may be arbitrary similar to malicious noise it constructs a hypothesis whose error rate on future examples is within an additive epsilon of the optimal halfspace in time poly n for any constant epsilon 0 for the uniform distribution over 1 1 n or unit sphere in mathbb r n as well as any log concave distribution in mathbb r n it also agnostically learns boolean disjunctions in time 2 tilde o sqrt n with respect to any distribution our algorithm which performs l 1 polynomial regression is a natural noise tolerant arbitrary distribution generalization of the well known low degree fourier algorithm of linial mansour and nisan we observe that significant improvements on the running time of our algorithm would yield the fastest known algorithm for learning parity with noise a challenging open problem in computational learning theory

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

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

using markov blankets for causal structure learning we show how a generic feature selection algorithm returning strongly relevant variables can be turned into a causal structure learning algorithm we prove this under the faithfulness assumption for the data distribution in a causal graph the strongly relevant variables for a node x are its parents children and children s parents or spouses also known as the markov blanket of x identifying the spouses leads to the detection of the v structure patterns and thus to causal orientations repeating the task for all variables yields a valid partially oriented causal graph we first show an efficient way to identify the spouse links we then perform several experiments in the continuous domain using the recursive feature elimination feature selection algorithm with support vector regression and empirically verify the intuition of this direct but computationally expensive approach within the same framework we then devise a fast and consistent algorithm total conditioning tc and a variant tcbw with an explicit backward feature selection heuristics for gaussian data after running a series of comparative experiments on five artificial networks we argue that markov blanket algorithms such as tc tcbw or grow shrink scale better than the reference pc algorithm and provides higher structural accuracy

estimating high dimensional intervention effects from observational data we assume that we have observational data generated from an unknown underlying directed acyclic graph dag model a dag is typically not identifiable from observational data but it is possible to consistently estimate the equivalence class of a dag moreover for any given dag causal effects can be estimated using intervention calculus in this paper we combine these two parts for each dag in the estimated equivalence class we use intervention calculus to estimate the causal effects of the covariates on the response this yields a collection of estimated causal effects for each covariate we show that the distinct values in this set can be consistently estimated by an algorithm that uses only local information of the graph this local approach is computationally fast and feasible in high dimensional problems we propose to use summary measures of the set of possible causal effects to determine variable importance in particular we use the minimum absolute value of this set since that is a lower bound on the size of the causal effect we demonstrate the merits of our methods in a simulation study and on a data set about riboflavin production

covariate selection for the nonparametric estimation of an average treatment effect observational studies in which the effect of a nonrandomized treatment on an outcome of interest is estimated are common in domains such as labour economics and epidemiology such studies often rel

special matchings calculate the parabolic kazhdan lusztig polynomials of the universal coxeter groups abstract in this paper we prove that the parabolic kazhdan lusztig polynomials and the parabolic r polynomials of the universal coxeter group can be computed in a combinatorial way by using special matchings

consistent feature selection for pattern recognition in polynomial time we analyze two different feature selection problems finding a minimal feature set optimal for classification minimal optimal vs finding all features relevant to the target variable all relevant the latter problem is motivated by recent applications within bioinformatics particularly gene expression analysis for both problems we identify classes of data distributions for which there exist consistent polynomial time algorithms we also prove that all relevant is much harder than minimal optimal and propose two consistent polynomial time algorithms we argue that the distribution classes considered are reasonable in many practical cases so that our results simplify feature selection in a wide range of machine learning tasks

quantum matchgate computations and linear threshold gates the theory of matchgates is of interest in various areas in physics and computer science matchgates occur for example in the study of fermions and spin chains in the theory of holographic algorithms and in several recent works in quantum computation in this paper we completely characterize the class of boolean functions computable by unitary two qubit matchgate circuits with some probability of success we show that this class precisely coincides with that of the linear threshold gates the latter is a fundamental family that appears in several fields such as the study of neural networks using the above characterization we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability in particular the only functions that are matchgate computable with success probability greater than 3 4 are functions depending on only a single bit of the input