arXiv subjects

Robin J. Evans

Publications and source records attributed to Robin J. Evans.

At least 37 records · Page 2Linked to original sources

arXiv2023

Doubly Robust Kernel Statistics for Testing Distributional Treatment Effects

With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem of testing for \emph{distributional} causal effects, where the treatment affects not just the mean, but also higher order moments of the distribution, as well as multidimensional or structured outcomes. We build upon a previously introduced framework, Counterfactual Mean Embeddings, for representing causal distributions within Reproducing Kernel Hilbert Spaces (RKHS) by proposing new, improved, estimators for the distributional embeddings. These improved estimators are inspired by doubly robust estimators of the causal mean, using a similar form within the kernel space. We analyse these estimators, proving they retain the doubly robust property and have improved convergence rates compared to the original estimators. This leads to new permutation based tests for distributional causal effects, using the estimators we propose as tests statistics. We experimentally and theoretically demonstrate the validity of our tests.

stat.ML↗

arXiv2023

Parameterizing and Simulating from Causal Models

Many statistical problems in causal inference involve a probability distribution other than the one from which data are actually observed; as an additional complication, the object of interest is often a marginal quantity of this other probability distribution. This creates many practical complications for statistical inference, even where the problem is non-parametrically identified. In particular, it is difficult to perform likelihood-based inference, or even to simulate from the model in a general way. We introduce the `frugal parameterization', which places the causal effect of interest at its centre, and then builds the rest of the model around it. We do this in a way that provides a recipe for constructing a regular, non-redundant parameterization using causal quantities of interest. In the case of discrete variables we can use odds ratios to complete the parameterization, while in the continuous case copulas are the natural choice; other possibilities are also discussed. Our methods allow us to construct and simulate from models with parametrically specified causal distributions, and fit them using likelihood-based methods, including fully Bayesian approaches. Our proposal includes parameterizations for the average causal effect and effect of treatment on the treated, as well as other causal quantities of interest.

stat.ME↗

arXiv2023

Nested Markov Properties for Acyclic Directed Mixed Graphs

Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation criterion), and the local Markov property. Marginals of DAG models also imply equality constraints that are not conditional independences; the well-known ``Verma constraint'' is an example. Constraints of this type are used for testing edges, and in a computationally efficient marginalization scheme via variable elimination. We show that equality constraints like the ``Verma constraint'' can be viewed as conditional independences in kernel objects obtained from joint distributions via a fixing operation that generalizes conditioning and marginalization. We use these constraints to define, via ordered local and global Markov properties, and a factorization, a graphical model associated with acyclic directed mixed graphs (ADMGs). We prove that marginal distributions of DAG models lie in this model, and that a set of these constraints given by Tian provides an alternative definition of the model. Finally, we show that the fixing operation used to define the model leads to a particularly simple characterization of identifiable causal effects in hidden variable causal DAG models.

stat.ME↗

arXiv2023

Results on Counterfactual Invariance

In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major question surrounding counterfactual invariance, how does it relate to conditional independence? We show that whilst counterfactual invariance implies conditional independence, conditional independence does not give any implications about the degree or likelihood of satisfying counterfactual invariance. Furthermore, we show that for discrete causal models counterfactually invariant functions are often constrained to be functions of particular variables, or even constant.

cs.LG↗

arXiv2023

PWSHAP: A Path-Wise Explanation Model for Targeted Variables

Predictive black-box models can exhibit high accuracy but their opaque nature hinders their uptake in safety-critical deployment environments. Explanation methods (XAI) can provide confidence for decision-making through increased transparency. However, existing XAI methods are not tailored towards models in sensitive domains where one predictor is of special interest, such as a treatment effect in a clinical model, or ethnicity in policy models. We introduce Path-Wise Shapley effects (PWSHAP), a framework for assessing the targeted effect of a binary (e.g.~treatment) variable from a complex outcome model. Our approach augments the predictive model with a user-defined directed acyclic graph (DAG). The method then uses the graph alongside on-manifold Shapley values to identify effects along causal pathways whilst maintaining robustness to adversarial attacks. We establish error bounds for the identified path-wise Shapley effects and for Shapley values. We show PWSHAP can perform local bias and mediation analyses with faithfulness to the model. Further, if the targeted variable is randomised we can quantify local effect modification. We demonstrate the resolution, interpretability, and true locality of our approach on examples and a real-world experiment.

stat.ML↗

arXiv2023

Latent-free equivalent mDAGs

We show that the marginal model for a discrete directed acyclic graph (DAG) with hidden variables is distributionally equivalent to another fully observable DAG model if and only if it does not induce any non-trivial inequality constraints.

math.ST↗

arXiv2022

Regression Identifiability and Edge Interventions in Linear Structural Equation Models

In this paper, we introduce a new identifiability criteria for linear structural equation models, which we call regression identifiability. We provide necessary and sufficient graphical conditions for a directed edge to be regression identifiable. Suppose $Σ^*$ corresponds to the covariance matrix of the graphical model $G^*$ obtained by performing an edge intervention to $G$ with corresponding covariance matrix $Σ$. We first obtain necessary and sufficient conditions for $Σ^*$ to be identifiable given $Σ$. Using regression identifiability, we obtain necessary graphical conditions for $Σ^*$ to be identifiable given $Σ$. We also identify what would happen to an individual data point if there were such an intervention. Finally, we provide some statistical problems where our methods could be used, such as finding constraints and simulating interventional data from observational data.

math.ST↗

arXiv2021

Rapid parameter estimation of a two-component neutron star model with spin wandering using a Kalman filter

The classic, two-component, crust-superfluid model of a neutron star can be formulated as a noise-driven, linear dynamical system, in which the angular velocities of the crust and superfluid are tracked using a Kalman filter applied to electromagnetic pulse timing data and gravitational wave data, when available. Here it is shown how to combine the marginal likelihood of the Kalman filter and nested sampling to estimate full posterior distributions of the six model parameters, extending previous analyses based on a maximum-likelihood approach. The method is tested across an astrophysically plausible parameter domain using Monte Carlo simulations. It recovers the injected parameters to $\lesssim 10$ per cent for time series containing $\sim 10^3$ samples, typical of long-term pulsar timing campaigns. It runs efficiently in $\mathcal O(1)$ CPU-hr for data sets of the above size. In a present-day observational scenario, when electromagnetic data are available only, the method accurately estimates three parameters: the relaxation time, the ensemble-averaged spin-down of the system, and the amplitude of the stochastic torques applied to the crust. In a future observational scenario, where gravitational wave data are also available, the method also estimates the ratio between the moments of inertia of the crust and the superfluid, the amplitude of the stochastic torque applied to the superfluid, and the crust-superfluid lag. These empirical results are consistent with a formal identifiability analysis of the linear dynamical system.

astro-ph.HE↗

arXiv2021

Dependency in DAG models with Hidden Variables

Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for two variables to be identically equal, while all other observed variables stay jointly independent of them and mutually of each other. We find that this is possible if and only if the two variables are `densely connected'; in other words, if applications of identifiable causal interventions on the graph cannot (non-trivially) separate them. As a consequence of this, we can also allow such pairs of random variables have any bivariate joint distribution that we choose. This has implications for model search, since it suggests that we can reduce to only consider graphs in which densely connected vertices are always joined by an edge.

math.ST↗

arXiv2019

Model selection and local geometry

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases---including common classes of causal or graphical models, as well as time series models---distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than the usual parametric $n^{-1/2}$ (typically we will require $n^{-1/4}$ or slower); in other words, to distinguish between the models we need large effect sizes or very large sample sizes. Second, we show that under even weaker conditions on their tangent cones, models in these classes cannot be made simultaneously convex by a reparameterization. This shows that Bayesian network models, amongst others, cannot be learned directly with a convex method similar to the graphical lasso. However, we are able to use our results to suggest methods for model selection that learn the tangent space directly, rather than the model itself. In particular, we give a generic algorithm for learning Bayesian network models.

math.ST↗

arXiv2019

Low-Voltage Distribution Network Impedances Identification Based on Smart Meter Data

Under conditions of high penetration of renewables, the low-voltage (LV) distribution network needs to be carefully managed. In such a scenario, an accurate real-time low-voltage power network model is an important prerequisite, which opens up the possibility for application of many advanced network control and optimisation methods thus providing improved power flow balancing, reduced maintenance costs, and enhanced reliability and security of a grid. Smart meters serve as a source of information in LV networks and allow for accurate measurements at almost every node, which makes it advantageous to use data driven methods. In this paper, we formulate a non-linear and non-convex problem, solve it efficiently, and propose a number of fully smart meter data driven methods for line parameters estimation. Our algorithms are fast, recursive in data, scale linearly with the number of nodes, and can be executed in a decentralised manner by running small algorithms inside each smart meter. The performance of these algorithms is demonstrated for different measurement accuracy scenarios through simulations.

math.OC↗

arXiv2018

Towards Characterising Bayesian Network Models under Selection

Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be from a distribution in a causal Bayesian network (BN) model under selection. Understanding the constraints in the model under selection is the first step towards recovering causal structure in the original model. The conditional-independence (CI) constraints in a BN model under selection have been already characterised; there exist, however, additional, non-CI constraints in such models. In this work, some initial results are provided that simplify the characterisation problem. In addition, an algorithm is designed for identifying compelled ancestors (definite causes) from a completed partially directed acyclic graph (CPDAG). Finally, a non-CI, non-factorisation constraint in a BN model under selection is computed for the first time.

math.ST↗

arXiv2017

Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams

We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and some sufficient conditions for distributional equivalence of BAPs which are used in an algorithmic ap- proach to compute (nearly) equivalent model structures. This allows us to infer lower bounds of causal effects. We also present applications to real and simulated datasets using our publicly available R-package.

stat.ML↗

arXiv2017

Margins of discrete Bayesian networks

Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular these two models have the same dimension. The nested Markov model is therefore the best possible description of the latent variable model that avoids consideration of inequalities, which are extremely complicated in general. A consequence of this is that the constraint finding algorithm of Tian and Pearl (UAI 2002, pp519-527) is complete for finding equality constraints. Latent variable models suffer from difficulties of unidentifiable parameters and non-regular asymptotics; in contrast the nested Markov model is fully identifiable, represents a curved exponential family of known dimension, and can easily be fitted using an explicit parameterization.

math.ST↗

arXiv2017

Smooth, identifiable supermodels of discrete DAG models with latent variables

We provide a parameterization of the discrete nested Markov model, which is a supermodel that approximates DAG models (Bayesian network models) with latent variables. Such models are widely used in causal inference and machine learning. We explicitly evaluate their dimension, show that they are curved exponential families of distributions, and fit them to data. The parameterization avoids the irregularities and unidentifiability of latent variable models. The parameters used are all fully identifiable and causally-interpretable quantities.

math.ST↗

arXiv2017

Lower Bounds on the Complexity of Solving Two Classes of Non-cooperative Games

This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game class is defined as the minimum number of iterations required to find a Nash equilibrium (NE) of any game in that class with $ε$ accuracy. First, we consider the class $\mathcal{G}$ of all $N$-player non-cooperative games with a continuous action space that admit at least one NE. Using information-theoretic inequalities, we derive a lower bound on the complexity of solving $\mathcal{G}$ that depends on the Kolmogorov $2ε$-capacity of the constraint set and the total capacity of the communication channels. We also derive a lower bound on the complexity of solving games in $\mathcal{G}$ which depends on the volume and surface area of the constraint set. We next consider the class of all $N$-player non-cooperative games with at least one NE such that the players' utility functions satisfy a certain (differential) constraint. We derive lower bounds on the complexity of solving this game class under both Gaussian and non-Gaussian noise models. Our result in the non-Gaussian case is derived by establishing a connection between the Kullback-Leibler distance and Fisher information.

cs.IT↗

arXiv2016

Modeling Website Visits

We propose a multivariate model for the number of hits on a set of popular websites, and show it to accurately reflect the behavior recorded in a data set of Internet users in the United States. We assume that the random vector of visits is distributed according to a censored multivariate normal with marginals transformed to be discrete Pareto IV and, following the ideas of Gaussian graphical models, we enforce sparsity on the inverse covariance matrix to reduce dimensionality and to visualize the dependence structure as a graph. The model allows for an easy inclusion of covariates and is useful for comprehending the behavior of Internet users as a function of their age and gender.

stat.AP↗

arXiv2016

Stochastic Geometry Methods for Modelling Automotive Radar Interference

As the use of automotive radar increases, performance limitations associated with radar-to-radar interference will become more significant. In this paper we employ tools from stochastic geometry to characterize the statistics of radar interference. Specifically, using two different models for vehicle spacial distributions, namely, a Poisson point process and a Bernoulli lattice process, we calculate for each case the interference statistics and obtain analytical expressions for the probability of successful range estimation. Our study shows that the regularity of the geometrical model appears to have limited effect on the interference statistics, and so it is possible to obtain tractable tight bounds for worst case performance. A technique is proposed for designing the duty cycle for random spectrum access which optimizes the total performance. This analytical framework is verified using Monte-Carlo simulations.

cs.IT↗