We characterize homotopical equivalences between causal DAG models, exploiting the close connections between partially ordered set representations of DAGs (posets) and finite Alexandroff topologies. Alexandroff spaces yield a directional topological space: the topology is defined by a unique minimal basis defined by an open set for each variable x, specified as the intersection of all open sets containing x. Alexandroff spaces induce a (reflexive, transitive) preorder. Alexandroff spaces satisfying the Kolmogorov T0 separation criterion, where open sets distinguish variables, converts the preordering into a partial ordering. Our approach broadly is to construct a topological representation of posets from data, and then use the poset representation to build a conventional DAG causal model. We illustrate our framework by showing how it unifies disparate algorithms and case studies proposed previously. Topology plays two key roles in causal discovery. First, topological separability constraints on datasets have been used in several previous approaches to infer causal structure from observations and interventions. Second, a diverse range ofgraphical models used to represent causal structures can be represented in a unified way in terms of a topological representation of the induced poset structure. We show that the homotopy theory of Alexandroff spaces can be exploited to significantly efficiently reduce the number of possible DAG structures, reducing the search space by several orders of magnitude.

Causal effect estimation for dynamic treatment regimes (DTRs) contributes to sequential decision making. However, censoring and time-dependent confounding under DTRs are challenging as the amount of observational data declines over time due to a reducing sample size but the feature dimension increases over time. Long-term follow-up compounds these challenges. Another challenge is the highly complex relationships between confounders, treatments, and outcomes, which causes the traditional and commonly used linear methods to fail. We combine outcome regression models with treatment models for high dimensional features using uncensored subjects that are small in sample size and we fit deep Bayesian models for outcome regression models to reveal the complex relationships between confounders, treatments, and outcomes. Also, the developed deep Bayesian models can model uncertainty and output the prediction variance which is essential for the safety-aware applications, such as self-driving cars and medical treatment design. The experimental results on medical simulations of HIV treatment show the ability of the proposed method to obtain stable and accurate dynamic causal effect estimation from observational data, especially with long-term follow-up. Our technique provides practical guidance for sequential decision making, and policy-making.

In recent years, machine learning (ML) algorithms have been deployed in safety-critical and high-stake decision-making, where the fairness of algorithms is of paramount importance. Fairness in ML centers on detecting bias towards certain demographic populations induced by an ML classifier and proposes algorithmic solutions to mitigate the bias with respect to different fairness definitions. To this end, several fairness verifiers have been proposed that compute the bias in the prediction of an ML classifier -- essentially beyond a finite dataset -- given the probability distribution of input features. In the context of verifying linear classifiers, existing fairness verifiers are limited by accuracy due to imprecise modelling of correlations among features and scalability due to restrictive formulations of the classifiers as SSAT or SMT formulas or by sampling. In this paper, we propose an efficient fairness verifier, called FVGM, that encodes the correlations among features as a Bayesian network. In contrast to existing verifiers, FVGM proposes a stochastic subset-sum based approach for verifying linear classifiers. Experimentally, we show that FVGM leads to an accurate and scalable assessment for more diverse families of fairness-enhancing algorithms, fairness attacks, and group/causal fairness metrics than the state-of-the-art. We also demonstrate that FVGM facilitates the computation of fairness influence functions as a stepping stone to detect the source of bias induced by subsets of features.

When humans are given a policy to execute, there can be policy execution errors and deviations in execution if there is uncertainty in identifying a state. So an algorithm that computes a policy for a human to execute ought to consider these effects in its computations. An optimal MDP policy that is poorly executed (because of a human agent) maybe much worse than another policy that is executed with fewer errors. In this paper, we consider the problems of erroneous execution and execution delay when computing policies for a human agent that would act in a setting modeled by a Markov Decision Process. We present a framework to model the likelihood of policy execution errors and likelihood of non-policy actions like inaction (delays) due to state uncertainty. This is followed by a hill climbing algorithm to search for good policies that account for these errors. We then use the best policy found by hill climbing with a branch and bound algorithm to find the optimal policy. We show experimental results in a Gridworld domain and analyze the performance of the two algorithms. We also present human studies that verify if our assumptions on policy execution by humans under state-aliasing are reasonable.

Autonomous marine vehicles play an essential role in many ocean science and engineering applications. Planning time and energy optimal paths for these vehicles to navigate in stochastic dynamic ocean environments is essential to reduce operational costs. In some missions, they must also harvest solar, wind, or wave energy (modeled as a stochastic scalar field) and move in optimal paths that minimize net energy consumption. Markov Decision Processes (MDPs) provide a natural framework for sequential decision-making for robotic agents in such environments. However, building a realistic model and solving the modeled MDP becomes computationally expensive in large-scale real-time applications, warranting the need for parallel algorithms and efficient implementation. In the present work, we introduce an efficient end-to-end GPU-accelerated algorithm that (i) builds the MDP model (computing transition probabilities and expected one-step rewards); and (ii) solves the MDP to compute an optimal policy. We develop methodical and algorithmic solutions to overcome the limited global memory of GPUs by (i) using a dynamic reduced-order representation of the ocean flows, (ii) leveraging the sparse nature of the state transition probability matrix, (iii) introducing a neighbouring sub-grid concept and (iv) proving that it is sufficient to use only the stochastic scalar field's mean to compute the expected one-step rewards for missions involving energy harvesting from the environment; thereby saving memory and reducing the computational effort. We demonstrate the algorithm on a simulated stochastic dynamic environment and highlight that it builds the MDP model and computes the optimal policy 600-1000x faster than conventional CPU implementations, making it suitable for real-time use.

We study a finite-horizon restless multi-armed bandit problem with multiple actions, dubbed R(MA)^2B. The state of each arm evolves according to a controlled Markov decision process (MDP), and the reward of pulling an arm depends on both the current state of the corresponding MDP and the action taken. The goal is to sequentially choose actions for arms so as to maximize the expected value of the cumulative rewards collected. Since finding the optimal policy is typically intractable, we propose a computationally appealing index policy which we call Occupancy-Measured-Reward Index Policy. Our policy is well-defined even if the underlying MDPs are not indexable. We prove that it is asymptotically optimal when the activation budget and number of arms are scaled up, while keeping their ratio as a constant. For the case when the system parameters are unknown, we develop a learning algorithm. Our learning algorithm uses the principle of optimism in the face of uncertainty and further uses a generative model in order to fully exploit the structure of Occupancy-Measured-Reward Index Policy. We call it the R(MA)^2B-UCB algorithm. As compared with the existing algorithms, R(MA)^2B-UCB performs close to an offline optimum policy, and also achieves a sub-linear regret with a low computational complexity. Experimental results show that R(MA)^2B-UCB outperforms the existing algorithms in both regret and run time.

The deep learning approach to detecting malicious software (malware) is promising but has yet to tackle the problem of dataset shift, namely that the joint distribution of examples and their labels associated with the test set is different from that of the training set. This problem causes the degradation of deep learning models without users' notice. In order to alleviate the problem, one approach is to let a classifier not only predict the label on a given example but also present its uncertainty (or confidence) on the predicted label, whereby a defender can decide whether to use the predicted label or not. While intuitive and clearly important, the capabilities and limitations of this approach have not been well understood. In this paper, we conduct an empirical study to evaluate the quality of predictive uncertainties of malware detectors. Specifically, we re-design and build 24 Android malware detectors (by transforming four off-the-shelf detectors with six calibration methods) and quantify their uncertainties with nine metrics, including three metrics dealing with data imbalance. Our main findings are: (i) predictive uncertainty indeed helps achieve reliable malware detection in the presence of dataset shift, but cannot cope with adversarial evasion attacks; (ii) approximate Bayesian methods are promising to calibrate and generalize malware detectors to deal with dataset shift, but cannot cope with adversarial evasion attacks; (iii) adversarial evasion attacks can render calibration methods useless, and it is an open problem to quantify the uncertainty associated with the predicted labels of adversarial examples (i.e., it is not effective to use predictive uncertainty to detect adversarial examples).

We investigate novel parameter estimation and goodness-of-fit (GOF) assessment methods for large-scale confirmatory item factor analysis (IFA) with many respondents, items, and latent factors. For parameter estimation, we extend Urban and Bauer's (2021) deep learning algorithm for exploratory IFA to the confirmatory setting by showing how to handle user-defined constraints on loadings and factor correlations. For GOF assessment, we explore new simulation-based tests and indices. In particular, we consider extensions of the classifier two-sample test (C2ST), a method that tests whether a machine learning classifier can distinguish between observed data and synthetic data sampled from a fitted IFA model. The C2ST provides a flexible framework that integrates overall model fit, piece-wise fit, and person fit. Proposed extensions include a C2ST-based test of approximate fit in which the user specifies what percentage of observed data can be distinguished from synthetic data as well as a C2ST-based relative fit index that is similar in spirit to the relative fit indices used in structural equation modeling. Via simulation studies, we first show that the confirmatory extension of Urban and Bauer's (2021) algorithm produces more accurate parameter estimates as the sample size increases and obtains comparable estimates to a state-of-the-art confirmatory IFA estimation procedure in less time. We next show that the C2ST-based test of approximate fit controls the empirical type I error rate and detects when the number of latent factors is misspecified. Finally, we empirically investigate how the sampling distribution of the C2ST-based relative fit index depends on the sample size.

All employees are expected to contribute to excellence through high quality research and teaching. The working environment for this position will be at CBU, in the Systems Biology & Machine Learning group headed by Prof. Tom Michoel. The aim of the INTRePID project is to create intelligent systems for personalized and precise risk prediction and diagnosis of non-communicable diseases using multi-omics data, by developing, implementing and validating novel algorithms for structure learning and inference in large-scale, multi-organ causal Bayesian gene networks. The project will have privileged access to a unique resource of multi-omics data from four Nordic countries generated by the project partners for a proof-of-concept application in cardiovascular medicine. The person appointed on this position will develop and apply models and algorithms for causal inference, graph representation learning, and inference in large-scale Bayesian networks.

EM (Expectation-Maximisation) Algorithm is the go to algorithm whenever we have to do parameter estimation with hidden variables, such as in hidden Markov Chains. For some reason, it is often poorly explained and students end up confused as to what exactly are we maximising in the E-step and M-steps. Here is my attempt at a (hopefully) clear and step by step explanation on exactly how EM Algorithm works.