arXiv subjects

Tom Heskes

Publications and source records attributed to Tom Heskes.

At least 37 records · Page 2Linked to original sources

arXiv2021

Learning Equational Theorem Proving

We develop Stratified Shortest Solution Imitation Learning (3SIL) to learn equational theorem proving in a deep reinforcement learning (RL) setting. The self-trained models achieve state-of-the-art performance in proving problems generated by one of the top open conjectures in quasigroup theory, the Abelian Inner Mapping (AIM) Conjecture. To develop the methods, we first use two simpler arithmetic rewriting tasks that share tree-structured proof states and sparse rewards with the AIM problems. On these tasks, 3SIL is shown to significantly outperform several established RL and imitation learning methods. The final system is then evaluated in a standalone and cooperative mode on the AIM problems. The standalone 3SIL-trained system proves in 60 seconds more theorems (70.2%) than the complex, hand-engineered Waldmeister system (65.5%). In the cooperative mode, the final system is combined with the Prover9 system, proving in 2 seconds what standalone Prover9 proves in 60 seconds.

cs.LG↗

arXiv2020

Spectral Ranking of Causal Influence in Complex Systems

Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors measure relevant process variables at appropriate sampling rates, to provide time series as primary sources for system diagnostics. However, high-dimensionality, non-linearity and non-stationarity of data remain a major challenge to effectively diagnose rare or new system issues by merely using model-based approaches. To reduce the causal search space, we validate an algorithm that applies transfer entropy to obtain a weighted directed graph from a system's multivariate time series and graph eigenvector centrality to identify the system's most influential parameters. The results suggest that this approach robustly identifies the true influential sources in a complex system, even when its information transfer network includes redundant edges.

cs.IT↗

arXiv2020

MASSIVE: Tractable and Robust Bayesian Learning of Many-Dimensional Instrumental Variable Models

The recent availability of huge, many-dimensional data sets, like those arising from genome-wide association studies (GWAS), provides many opportunities for strengthening causal inference. One popular approach is to utilize these many-dimensional measurements as instrumental variables (instruments) for improving the causal effect estimate between other pairs of variables. Unfortunately, searching for proper instruments in a many-dimensional set of candidates is a daunting task due to the intractable model space and the fact that we cannot directly test which of these candidates are valid, so most existing search methods either rely on overly stringent modeling assumptions or fail to capture the inherent model uncertainty in the selection process. We show that, as long as at least some of the candidates are (close to) valid, without knowing a priori which ones, they collectively still pose enough restrictions on the target interaction to obtain a reliable causal effect estimate. We propose a general and efficient causal inference algorithm that accounts for model uncertainty by performing Bayesian model averaging over the most promising many-dimensional instrumental variable models, while at the same time employing weaker assumptions regarding the data generating process. We showcase the efficiency, robustness and predictive performance of our algorithm through experimental results on both simulated and real-world data.

stat.ML↗

arXiv2020

Inferring the Direction of a Causal Link and Estimating Its Effect via a Bayesian Mendelian Randomization Approach

The use of genetic variants as instrumental variables - an approach known as Mendelian randomization - is a popular epidemiological method for estimating the causal effect of an exposure (phenotype, biomarker, risk factor) on a disease or health-related outcome from observational data. Instrumental variables must satisfy strong, often untestable assumptions, which means that finding good genetic instruments among a large list of potential candidates is challenging. This difficulty is compounded by the fact that many genetic variants influence more than one phenotype through different causal pathways, a phenomenon called horizontal pleiotropy. This leads to errors not only in estimating the magnitude of the causal effect but also in inferring the direction of the putative causal link. In this paper, we propose a Bayesian approach called BayesMR that is a generalization of the Mendelian randomization technique in which we allow for pleiotropic effects and, crucially, for the possibility of reverse causation. The output of the method is a posterior distribution over the target causal effect, which provides an immediate and easily interpretable measure of the uncertainty in the estimation. More importantly, we use Bayesian model averaging to determine how much more likely the inferred direction is relative to the reverse direction.

stat.ME↗

arXiv2020

Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models

Shapley values underlie one of the most popular model-agnostic methods within explainable artificial intelligence. These values are designed to attribute the difference between a model's prediction and an average baseline to the different features used as input to the model. Being based on solid game-theoretic principles, Shapley values uniquely satisfy several desirable properties, which is why they are increasingly used to explain the predictions of possibly complex and highly non-linear machine learning models. Shapley values are well calibrated to a user's intuition when features are independent, but may lead to undesirable, counterintuitive explanations when the independence assumption is violated. In this paper, we propose a novel framework for computing Shapley values that generalizes recent work that aims to circumvent the independence assumption. By employing Pearl's do-calculus, we show how these 'causal' Shapley values can be derived for general causal graphs without sacrificing any of their desirable properties. Moreover, causal Shapley values enable us to separate the contribution of direct and indirect effects. We provide a practical implementation for computing causal Shapley values based on causal chain graphs when only partial information is available and illustrate their utility on a real-world example.

cs.AI↗

arXiv2019

Constraining the Parameters of High-Dimensional Models with Active Learning

Constraining the parameters of physical models with $>5-10$ parameters is a widespread problem in fields like particle physics and astronomy. The generation of data to explore this parameter space often requires large amounts of computational resources. The commonly used solution of reducing the number of relevant physical parameters hampers the generality of the results. In this paper we show that this problem can be alleviated by the use of active learning. We illustrate this with examples from high energy physics, a field where simulations are often expensive and parameter spaces are high-dimensional. We show that the active learning techniques query-by-committee and query-by-dropout-committee allow for the identification of model points in interesting regions of high-dimensional parameter spaces (e.g. around decision boundaries). This makes it possible to constrain model parameters more efficiently than is currently done with the most common sampling algorithms and to train better performing machine learning models on the same amount of data. Code implementing the experiments in this paper can be found on GitHub.

cs.LG↗

arXiv2019

Large-Scale Local Causal Inference of Gene Regulatory Relationships

Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput genetic data. Many of these computational methods are designed to infer individual regulatory relationships among genes from data on gene expression. We propose a novel efficient Bayesian method for discovering local causal relationships among triplets of (normally distributed) variables. In our approach, we score covariance structures for each triplet in one go and incorporate available background knowledge in the form of priors to derive posterior probabilities over local causal structures. Our method is flexible in the sense that it allows for different types of causal structures and assumptions. We apply our approach to the task of learning causal regulatory relationships among genes. We show that the proposed algorithm produces stable and conservative posterior probability estimates over local causal structures that can be used to derive an honest ranking of the most meaningful regulatory relationships. We demonstrate the stability and efficacy of our method both on simulated data and on real-world data from an experiment on yeast.

stat.ML↗

arXiv2018

A Bayesian Approach for Inferring Local Causal Structure in Gene Regulatory Networks

Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput genetic data. A typical approach consists of a series of conditional independence tests on the covariance structure meant to progressively reduce the space of possible causal models. We propose a novel efficient Bayesian method for discovering the local causal relationships among triplets of (normally distributed) variables. In our approach, we score the patterns in the covariance matrix in one go and we incorporate the available background knowledge in the form of priors over causal structures. Our method is flexible in the sense that it allows for different types of causal structures and assumptions. We apply the approach to the task of inferring gene regulatory networks by learning regulatory relationships between gene expression levels. We show that our algorithm produces stable and conservative posterior probability estimates over local causal structures that can be used to derive an honest ranking of the most meaningful regulatory relationships. We demonstrate the stability and efficacy of our method both on simulated data and on real-world data from an experiment on yeast.

stat.ML↗

arXiv2018

A Novel Bayesian Approach for Latent Variable Modeling from Mixed Data with Missing Values

We consider the problem of learning parameters of latent variable models from mixed (continuous and ordinal) data with missing values. We propose a novel Bayesian Gaussian copula factor (BGCF) approach that is consistent under certain conditions and that is quite robust to the violations of these conditions. In simulations, BGCF substantially outperforms two state-of-the-art alternative approaches. An illustration on the `Holzinger & Swineford 1939' dataset indicates that BGCF is favorable over the so-called robust maximum likelihood (MLR) even if the data match the assumptions of MLR.

stat.ML↗

arXiv2018

Stable specification search in structural equation model with latent variables

In our previous study, we introduced stable specification search for cross-sectional data (S3C). It is an exploratory causal method that combines stability selection concept and multi-objective optimization to search for stable and parsimonious causal structures across the entire range of model complexities. In this study, we extended S3C to S3C-Latent, to model causal relations between latent variables. We evaluated S3C-Latent on simulated data and compared the results to those of PC-MIMBuild, an extension of the PC algorithm, the state-of-the-art causal discovery method. The comparison showed that S3C-Latent achieved better performance. We also applied S3C-Latent to real-world data of children with attention deficit/hyperactivity disorder and data about measuring mental abilities among pupils. The results are consistent with those of previous studies.

stat.ML↗

arXiv2017

Convolutional Neural Networks for Transient Candidate Vetting in Large-Scale Surveys

Current synoptic sky surveys monitor large areas of the sky to find variable and transient astronomical sources. As the number of detections per night at a single telescope easily exceeds several thousand, current detection pipelines make intensive use of machine learning algorithms to classify the detected objects and to filter out the most interesting candidates. A number of upcoming surveys will produce up to three orders of magnitude more data, which renders high-precision classification systems essential to reduce the manual and, hence, expensive vetting by human experts. We present an approach based on convolutional neural networks to discriminate between true astrophysical sources and artefacts in reference-subtracted optical images. We show that relatively simple networks are already competitive with state-of-the-art systems and that their quality can further be improved via slightly deeper networks and additional preprocessing steps -- eventually yielding models outperforming state-of-the-art systems. In particular, our best model correctly classifies about 97.3% of all 'real' and 99.7% of all 'bogus' instances on a test set containing 1,942 'bogus' and 227 'real' instances in total. Furthermore, the networks considered in this work can also successfully classify these objects at hand without relying on difference images, which might pave the way for future detection pipelines not containing image subtraction steps at all.

astro-ph.IM↗

arXiv2017

Robust Causal Estimation in the Large-Sample Limit without Strict Faithfulness

Causal effect estimation from observational data is an important and much studied research topic. The instrumental variable (IV) and local causal discovery (LCD) patterns are canonical examples of settings where a closed-form expression exists for the causal effect of one variable on another, given the presence of a third variable. Both rely on faithfulness to infer that the latter only influences the target effect via the cause variable. In reality, it is likely that this assumption only holds approximately and that there will be at least some form of weak interaction. This brings about the paradoxical situation that, in the large-sample limit, no predictions are made, as detecting the weak edge invalidates the setting. We introduce an alternative approach by replacing strict faithfulness with a prior that reflects the existence of many 'weak' (irrelevant) and 'strong' interactions. We obtain a posterior distribution over the target causal effect estimator which shows that, in many cases, we can still make good estimates. We demonstrate the approach in an application on a simple linear-Gaussian setting, using the MultiNest sampling algorithm, and compare it with established techniques to show our method is robust even when strict faithfulness is violated.

stat.ML↗

arXiv2017

Causality on Longitudinal Data: Stable Specification Search in Constrained Structural Equation Modeling

A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for longitudinal data, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Our approach uses exploratory search but allows incorporation of prior knowledge, e.g., the absence of a particular causal relationship between two specific variables. We represent causal relationships using structural equation models. Models are scored along two objectives: the model fit and the model complexity. Since both objectives are often conflicting we apply a multi-objective evolutionary algorithm to search for Pareto optimal models. To handle the instability of small finite data samples, we repeatedly subsample the data and select those substructures (from the optimal models) that are both stable and parsimonious. These substructures can be visualized through a causal graph. Our more exploratory approach achieves at least comparable performance as, but often a significant improvement over state-of-the-art alternative approaches on a simulated data set with a known ground truth. We also present the results of our method on three real-world longitudinal data sets on chronic fatigue syndrome, Alzheimer disease, and chronic kidney disease. The findings obtained with our approach are generally in line with results from more hypothesis-driven analyses in earlier studies and suggest some novel relationships that deserve further research.

stat.ML↗

arXiv2016

Location Sensitive Deep Convolutional Neural Networks for Segmentation of White Matter Hyperintensities

The anatomical location of imaging features is of crucial importance for accurate diagnosis in many medical tasks. Convolutional neural networks (CNN) have had huge successes in computer vision, but they lack the natural ability to incorporate the anatomical location in their decision making process, hindering success in some medical image analysis tasks. In this paper, to integrate the anatomical location information into the network, we propose several deep CNN architectures that consider multi-scale patches or take explicit location features while training. We apply and compare the proposed architectures for segmentation of white matter hyperintensities in brain MR images on a large dataset. As a result, we observe that the CNNs that incorporate location information substantially outperform a conventional segmentation method with hand-crafted features as well as CNNs that do not integrate location information. On a test set of 46 scans, the best configuration of our networks obtained a Dice score of 0.791, compared to 0.797 for an independent human observer. Performance levels of the machine and the independent human observer were not statistically significantly different (p-value=0.17).

cs.CV↗

arXiv2016

Deep Multi-scale Location-aware 3D Convolutional Neural Networks for Automated Detection of Lacunes of Presumed Vascular Origin

Lacunes of presumed vascular origin (lacunes) are associated with an increased risk of stroke, gait impairment, and dementia and are a primary imaging feature of the small vessel disease. Quantification of lacunes may be of great importance to elucidate the mechanisms behind neuro-degenerative disorders and is recommended as part of study standards for small vessel disease research. However, due to the different appearance of lacunes in various brain regions and the existence of other similar-looking structures, such as perivascular spaces, manual annotation is a difficult, elaborative and subjective task, which can potentially be greatly improved by reliable and consistent computer-aided detection (CAD) routines. In this paper, we propose an automated two-stage method using deep convolutional neural networks (CNN). We show that this method has good performance and can considerably benefit readers. We first use a fully convolutional neural network to detect initial candidates. In the second step, we employ a 3D CNN as a false positive reduction tool. As the location information is important to the analysis of candidate structures, we further equip the network with contextual information using multi-scale analysis and integration of explicit location features. We trained, validated and tested our networks on a large dataset of 1075 cases obtained from two different studies. Subsequently, we conducted an observer study with four trained observers and compared our method with them using a free-response operating characteristic analysis. Shown on a test set of 111 cases, the resulting CAD system exhibits performance similar to the trained human observers and achieves a sensitivity of 0.974 with 0.13 false positives per slice. A feasibility study also showed that a trained human observer would considerably benefit once aided by the CAD system.

cs.CV↗

arXiv2016

The Artificial Mind's Eye: Resisting Adversarials for Convolutional Neural Networks using Internal Projection

We introduce a novel artificial neural network architecture that integrates robustness to adversarial input in the network structure. The main idea of our approach is to force the network to make predictions on what the given instance of the class under consideration would look like and subsequently test those predictions. By forcing the network to redraw the relevant parts of the image and subsequently comparing this new image to the original, we are having the network give a "proof" of the presence of the object.

cs.LG↗

arXiv2016

Causality on Cross-Sectional Data: Stable Specification Search in Constrained Structural Equation Modeling

Causal modeling has long been an attractive topic for many researchers and in recent decades there has seen a surge in theoretical development and discovery algorithms. Generally discovery algorithms can be divided into two approaches: constraint-based and score-based. The constraint-based approach is able to detect common causes of the observed variables but the use of independence tests makes it less reliable. The score-based approach produces a result that is easier to interpret as it also measures the reliability of the inferred causal relationships, but it is unable to detect common confounders of the observed variables. A drawback of both score-based and constrained-based approaches is the inherent instability in structure estimation. With finite samples small changes in the data can lead to completely different optimal structures. The present work introduces a new hypothesis-free score-based causal discovery algorithm, called stable specification search, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Structure search is performed over Structural Equation Models. Our approach uses exploratory search but allows incorporation of prior background knowledge. We validated our approach on one simulated data set, which we compare to the known ground truth, and two real-world data sets for Chronic Fatigue Syndrome and Attention Deficit Hyperactivity Disorder, which we compare to earlier medical studies. The results on the simulated data set show significant improvement over alternative approaches and the results on the real-word data sets show consistency with the hypothesis driven models constructed by medical experts.

stat.ML↗

arXiv2016

Regularizing Solutions to the MEG Inverse Problem Using Space-Time Separable Covariance Functions

In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by regularizing the solution in space and time by a Gaussian process (Gaussian random field) model. Assuming a separable covariance function in space and time, the computational complexity of the proposed model becomes (without any further assumptions or restrictions) $\mathcal{O}(t^3 + n^3 + m^2n)$, where $t$ is the number of time steps, $m$ is the number of sources, and $n$ is the number of sensors. We apply the method to both simulated and empirical data, and demonstrate the efficiency and generality of our Bayesian source reconstruction approach which subsumes various classical approaches in the literature.

stat.AP↗