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We consider the problem of estimating the transition dynamics $T^*$ from near-optimal expert trajectories in the context of offline model-based reinforcement learning. We develop a novel constraint-based method, Inverse Transition Learning, that treats the limited coverage of the expert trajectories as a \emph{feature}: we use the fact that the expert is near-optimal to inform our estimate of $T^*$. We integrate our constraints into a Bayesian approach. Across both synthetic environments and real healthcare scenarios like Intensive Care Unit (ICU) patient management in hypotension, we demonstrate not only significant improvements in decision-making, but that our posterior can inform when transfer will be successful.

Large language models (LLMs) trained with Reinforcement Learning from Human Feedback (RLHF) have demonstrated remarkable capabilities, but their underlying reward functions and decision-making processes remain opaque. This paper introduces a novel approach to interpreting LLMs by applying inverse reinforcement learning (IRL) to recover their implicit reward functions. We conduct experiments on toxicity-aligned LLMs of varying sizes, extracting reward models that achieve up to 80.40% accuracy in predicting human preferences. Our analysis reveals key insights into the non-identifiability of reward functions, the relationship between model size and interpretability, and potential pitfalls in the RLHF process. We demonstrate that IRL-derived reward models can be used to fine-tune new LLMs, resulting in comparable or improved performance on toxicity benchmarks. This work provides a new lens for understanding and improving LLM alignment, with implications for the responsible development and deployment of these powerful systems., Comment: Preprint

Within batch reinforcement learning, safe policy improvement (SPI) seeks to ensure that the learnt policy performs at least as well as the behavior policy that generated the dataset. The core challenge in SPI is seeking improvements while balancing risk when many state-action pairs may be infrequently visited. In this work, we introduce Decision Points RL (DPRL), an algorithm that restricts the set of state-action pairs (or regions for continuous states) considered for improvement. DPRL ensures high-confidence improvement in densely visited states (i.e. decision points) while still utilizing data from sparsely visited states. By appropriately limiting where and how we may deviate from the behavior policy, we achieve tighter bounds than prior work; specifically, our data-dependent bounds do not scale with the size of the state and action spaces. In addition to the analysis, we demonstrate that DPRL is both safe and performant on synthetic and real datasets.

As AI models grow larger, the demand for accountability and interpretability has become increasingly critical for understanding their decision-making processes. Concept Bottleneck Models (CBMs) have gained attention for enhancing interpretability by mapping inputs to intermediate concepts before making final predictions. However, CBMs often suffer from information leakage, where additional input data, not captured by the concepts, is used to improve task performance, complicating the interpretation of downstream predictions. In this paper, we introduce a novel approach for training both joint and sequential CBMs that allows us to identify and control leakage using decision trees. Our method quantifies leakage by comparing the decision paths of hard CBMs with their soft, leaky counterparts. Specifically, we show that soft leaky CBMs extend the decision paths of hard CBMs, particularly in cases where concept information is incomplete. Using this insight, we develop a technique to better inspect and manage leakage, isolating the subsets of data most affected by this. Through synthetic and real-world experiments, we demonstrate that controlling leakage in this way not only improves task accuracy but also yields more informative and transparent explanations.

Machine learning (ML) models can make decisions based on large amounts of data, but they can be missing personal knowledge available to human users about whom predictions are made. For example, a model trained to predict psychiatric outcomes may know nothing about a patient's social support system, and social support may look different for different patients. In this work, we introduce the problem of human feature integration, which provides a way to incorporate important personal-knowledge from users without domain expertise into ML predictions. We characterize this problem through illustrative user stories and comparisons to existing approaches; we formally describe this problem in a way that paves the ground for future technical solutions; and we provide a proof-of-concept study of a simple version of a solution to this problem in a semi-realistic setting.

Interpretability methods that utilise local surrogate models (e.g. LIME) are very good at describing the behaviour of the predictive model at a point of interest, but they are not guaranteed to extrapolate to the local region surrounding the point. However, overfitting to the local curvature of the predictive model and malicious tampering can significantly limit extrapolation. We propose an anchor-based algorithm for identifying regions in which local explanations are guaranteed to be correct by explicitly describing those intervals along which the input features can be trusted. Our method produces an interpretable feature-aligned box where the prediction of the local surrogate model is guaranteed to match the predictive model. We demonstrate that our algorithm can be used to find explanations with larger guarantee regions that better cover the data manifold compared to existing baselines. We also show how our method can identify misleading local explanations with significantly poorer guarantee regions.

Intrusion research frequently collects data on attack techniques currently employed and their potential symptoms. This includes deploying honeypots, logging events from existing devices, employing a red team for a sample attack campaign, or simulating system activity. However, these observational studies do not clearly discern the cause-and-effect relationships between the design of the environment and the data recorded. Neglecting such relationships increases the chance of drawing biased conclusions due to unconsidered factors, such as spurious correlations between features and errors in measurement or classification. In this paper, we present the theory and empirical data on methods that aim to discover such causal relationships efficiently. Our adaptive design (AD) is inspired by the clinical trial community: a variant of a randomized control trial (RCT) to measure how a particular ``treatment'' affects a population. To contrast our method with observational studies and RCT, we run the first controlled and adaptive honeypot deployment study, identifying the causal relationship between an ssh vulnerability and the rate of server exploitation. We demonstrate that our AD method decreases the total time needed to run the deployment by at least 33%, while still confidently stating the impact of our change in the environment. Compared to an analogous honeypot study with a control group, our AD requests 17% fewer honeypots while collecting 19% more attack recordings than an analogous honeypot study with a control group., Comment: CAMLIS'23 Pre-publication - TO BE UPDATED!!

Offline Reinforcement learning is commonly used for sequential decision-making in domains such as healthcare and education, where the rewards are known and the transition dynamics $T$ must be estimated on the basis of batch data. A key challenge for all tasks is how to learn a reliable estimate of the transition dynamics $T$ that produce near-optimal policies that are safe enough so that they never take actions that are far away from the best action with respect to their value functions and informative enough so that they communicate the uncertainties they have. Using data from an expert, we propose a new constraint-based approach that captures our desiderata for reliably learning a posterior distribution of the transition dynamics $T$ that is free from gradients. Our results demonstrate that by using our constraints, we learn a high-performing policy, while considerably reducing the policy's variance over different datasets. We also explain how combining uncertainty estimation with these constraints can help us infer a partial ranking of actions that produce higher returns, and helps us infer safer and more informative policies for planning., Comment: 8 pages, 1 plots, 2 tables

Off-policy evaluation (OPE) aims to estimate the benefit of following a counterfactual sequence of actions, given data collected from executed sequences. However, existing OPE estimators often exhibit high bias and high variance in problems involving large, combinatorial action spaces. We investigate how to mitigate this issue using factored action spaces i.e. expressing each action as a combination of independent sub-actions from smaller action spaces. This approach facilitates a finer-grained analysis of how actions differ in their effects. In this work, we propose a new family of "decomposed" importance sampling (IS) estimators based on factored action spaces. Given certain assumptions on the underlying problem structure, we prove that the decomposed IS estimators have less variance than their original non-decomposed versions, while preserving the property of zero bias. Through simulations, we empirically verify our theoretical results, probing the validity of various assumptions. Provided with a technique that can derive the action space factorisation for a given problem, our work shows that OPE can be improved "for free" by utilising this inherent problem structure., Comment: Main paper: 8 pages, 7 figures. Appendix: 30 pages, 17 figures. Accepted at ICML 2023 Workshop on Counterfactuals in Minds and Machines, Honolulu, Hawaii, USA. Camera ready version

Discount regularization, using a shorter planning horizon when calculating the optimal policy, is a popular choice to restrict planning to a less complex set of policies when estimating an MDP from sparse or noisy data (Jiang et al., 2015). It is commonly understood that discount regularization functions by de-emphasizing or ignoring delayed effects. In this paper, we reveal an alternate view of discount regularization that exposes unintended consequences. We demonstrate that planning under a lower discount factor produces an identical optimal policy to planning using any prior on the transition matrix that has the same distribution for all states and actions. In fact, it functions like a prior with stronger regularization on state-action pairs with more transition data. This leads to poor performance when the transition matrix is estimated from data sets with uneven amounts of data across state-action pairs. Our equivalence theorem leads to an explicit formula to set regularization parameters locally for individual state-action pairs rather than globally. We demonstrate the failures of discount regularization and how we remedy them using our state-action-specific method across simple empirical examples as well as a medical cancer simulator.

Decision-focused (DF) model-based reinforcement learning has recently been introduced as a powerful algorithm that can focus on learning the MDP dynamics that are most relevant for obtaining high returns. While this approach increases the agent's performance by directly optimizing the reward, it does so by learning less accurate dynamics from a maximum likelihood perspective. We demonstrate that when the reward function is defined by preferences over multiple objectives, the DF model may be sensitive to changes in the objective preferences.In this work, we develop the robust decision-focused (RDF) algorithm, which leverages the non-identifiability of DF solutions to learn models that maximize expected returns while simultaneously learning models that transfer to changes in the preference over multiple objectives. We demonstrate the effectiveness of RDF on two synthetic domains and two healthcare simulators, showing that it significantly improves the robustness of DF model learning to changes in the reward function without compromising training-time return.

In safety-critical decision-making scenarios being able to identify worst-case outcomes, or dead-ends is crucial in order to develop safe and reliable policies in practice. These situations are typically rife with uncertainty due to unknown or stochastic characteristics of the environment as well as limited offline training data. As a result, the value of a decision at any time point should be based on the distribution of its anticipated effects. We propose a framework to identify worst-case decision points, by explicitly estimating distributions of the expected return of a decision. These estimates enable earlier indication of dead-ends in a manner that is tunable based on the risk tolerance of the designed task. We demonstrate the utility of Distributional Dead-end Discovery (DistDeD) in a toy domain as well as when assessing the risk of severely ill patients in the intensive care unit reaching a point where death is unavoidable. We find that DistDeD significantly improves over prior discovery approaches, providing indications of the risk 10 hours earlier on average as well as increasing detection by 20%., Comment: To appear in TMLR (01/2023). The submission and reviews can be viewed at: https://openreview.net/forum?id=oKlEOT83gI

We develop a Reinforcement Learning (RL) framework for improving an existing behavior policy via sparse, user-interpretable changes. Our goal is to make minimal changes while gaining as much benefit as possible. We define a minimal change as having a sparse, global contrastive explanation between the original and proposed policy. We improve the current policy with the constraint of keeping that global contrastive explanation short. We demonstrate our framework with a discrete MDP and a continuous 2D navigation domain., Comment: Accepted at IMLH Workshop, ICML 2022

Assessing the effects of a policy based on observational data from a different policy is a common problem across several high-stake decision-making domains, and several off-policy evaluation (OPE) techniques have been proposed. However, these methods largely formulate OPE as a problem disassociated from the process used to generate the data (i.e. structural assumptions in the form of a causal graph). We argue that explicitly highlighting this association has important implications on our understanding of the fundamental limits of OPE. First, this implies that current formulation of OPE corresponds to a narrow set of tasks, i.e. a specific causal estimand which is focused on prospective evaluation of policies over populations or sub-populations. Second, we demonstrate how this association motivates natural desiderata to consider a general set of causal estimands, particularly extending the role of OPE for counterfactual off-policy evaluation at the level of individuals of the population. A precise description of the causal estimand highlights which OPE estimands are identifiable from observational data under the stated generative assumptions. For those OPE estimands that are not identifiable, the causal perspective further highlights where more experimental data is necessary, and highlights situations where human expertise can aid identification and estimation. Furthermore, many formalisms of OPE overlook the role of uncertainty entirely in the estimation process.We demonstrate how specifically characterising the causal estimand highlights the different sources of uncertainty and when human expertise can naturally manage this uncertainty. We discuss each of these aspects as actionable desiderata for future OPE research at scale and in-line with practical utility.

Identifying meaningful and independent factors of variation in a dataset is a challenging learning task frequently addressed by means of deep latent variable models. This task can be viewed as learning symmetry transformations preserving the value of a chosen property along latent dimensions. However, existing approaches exhibit severe drawbacks in enforcing the invariance property in the latent space. We address these shortcomings with a novel approach to cycle consistency. Our method involves two separate latent subspaces for the target property and the remaining input information, respectively. In order to enforce invariance as well as sparsity in the latent space, we incorporate semantic knowledge by using cycle consistency constraints relying on property side information. The proposed method is based on the deep information bottleneck and, in contrast to other approaches, allows using continuous target properties and provides inherent model selection capabilities. We demonstrate on synthetic and molecular data that our approach identifies more meaningful factors which lead to sparser and more interpretable models with improved invariance properties., Comment: 16 pages, 3 figures, published at the DAGM German Conference on Pattern Recognition, Sep. 28 - Oct. 1, 2021

Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify discrete components in the data. In this work, we focus on a constrained capacity setting, where we want to learn a model with relatively few components (e.g. for interpretability purposes). To maintain prediction performance, we introduce prediction-focused modeling for mixtures, which automatically selects the dimensions relevant to the prediction task. Our approach identifies relevant signal from the input, outperforms models that are not prediction-focused, and is easy to optimize; we also characterize when prediction-focused modeling can be expected to work.

Machine learning models that utilize patient data across time (rather than just the most recent measurements) have increased performance for many risk stratification tasks in the intensive care unit. However, many of these models and their learned representations are complex and therefore difficult for clinicians to interpret, creating challenges for validation. Our work proposes a new procedure to learn summaries of clinical time-series that are both predictive and easily understood by humans. Specifically, our summaries consist of simple and intuitive functions of clinical data (e.g. falling mean arterial pressure). Our learned summaries outperform traditional interpretable model classes and achieve performance comparable to state-of-the-art deep learning models on an in-hospital mortality classification task., Comment: 10 pages, 3 figures, AMIA 2021 Annual Symposium

Learning-to-defer is a framework to automatically defer decision-making to a human expert when ML-based decisions are deemed unreliable. Existing learning-to-defer frameworks are not designed for sequential settings. That is, they defer at every instance independently, based on immediate predictions, while ignoring the potential long-term impact of these interventions. As a result, existing frameworks are myopic. Further, they do not defer adaptively, which is crucial when human interventions are costly. In this work, we propose Sequential Learning-to-Defer (SLTD), a framework for learning-to-defer to a domain expert in sequential decision-making settings. Contrary to existing literature, we pose the problem of learning-to-defer as model-based reinforcement learning (RL) to i) account for long-term consequences of ML-based actions using RL and ii) adaptively defer based on the dynamics (model-based). Our proposed framework determines whether to defer (at each time step) by quantifying whether a deferral now will improve the value compared to delaying deferral to the next time step. To quantify the improvement, we account for potential future deferrals. As a result, we learn a pre-emptive deferral policy (i.e. a policy that defers early if using the ML-based policy could worsen long-term outcomes). Our deferral policy is adaptive to the non-stationarity in the dynamics. We demonstrate that adaptive deferral via SLTD provides an improved trade-off between long-term outcomes and deferral frequency on synthetic, semi-synthetic, and real-world data with non-stationary dynamics. Finally, we interpret the deferral decision by decomposing the propagated (long-term) uncertainty around the outcome, to justify the deferral decision.

Estimating an individual's potential response to interventions from observational data is of high practical relevance for many domains, such as healthcare, public policy or economics. In this setting, it is often the case that combinations of interventions may be applied simultaneously, for example, multiple prescriptions in healthcare or different fiscal and monetary measures in economics. However, existing methods for counterfactual inference are limited to settings in which actions are not used simultaneously. Here, we present Neural Counterfactual Relation Estimation (NCoRE), a new method for learning counterfactual representations in the combination treatment setting that explicitly models cross-treatment interactions. NCoRE is based on a novel branched conditional neural representation that includes learnt treatment interaction modulators to infer the potential causal generative process underlying the combination of multiple treatments. Our experiments show that NCoRE significantly outperforms existing state-of-the-art methods for counterfactual treatment effect estimation that do not account for the effects of combining multiple treatments across several synthetic, semi-synthetic and real-world benchmarks.

We propose Preferential MoE, a novel human-ML mixture-of-experts model that augments human expertise in decision making with a data-based classifier only when necessary for predictive performance. Our model exhibits an interpretable gating function that provides information on when human rules should be followed or avoided. The gating function is maximized for using human-based rules, and classification errors are minimized. We propose solving a coupled multi-objective problem with convex subproblems. We develop approximate algorithms and study their performance and convergence. Finally, we demonstrate the utility of Preferential MoE on two clinical applications for the treatment of Human Immunodeficiency Virus (HIV) and management of Major Depressive Disorder (MDD)., Comment: 10 pages, 5 figures, 4 tables, AMIA 2021 Virtual Informatics Summit

Coronavirus Disease 2019 (COVID-19) is an emerging respiratory disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) with rapid human-to-human transmission and a high case fatality rate particularly in older patients. Due to the exponential growth of infections, many healthcare systems across the world are under pressure to care for increasing amounts of at-risk patients. Given the high number of infected patients, identifying patients with the highest mortality risk early is critical to enable effective intervention and optimal prioritisation of care. Here, we present the COVID-19 Early Warning System (CovEWS), a clinical risk scoring system for assessing COVID-19 related mortality risk. CovEWS provides continuous real-time risk scores for individual patients with clinically meaningful predictive performance up to 192 hours (8 days) in advance, and is automatically derived from patients' electronic health records (EHRs) using machine learning. We trained and evaluated CovEWS using de-identified data from a cohort of 66430 COVID-19 positive patients seen at over 69 healthcare institutions in the United States (US), Australia, Malaysia and India amounting to an aggregated total of over 2863 years of patient observation time. On an external test cohort of 5005 patients, CovEWS predicts COVID-19 related mortality from $78.8\%$ ($95\%$ confidence interval [CI]: $76.0$, $84.7\%$) to $69.4\%$ ($95\%$ CI: $57.6, 75.2\%$) specificity at a sensitivity greater than $95\%$ between respectively 1 and 192 hours prior to observed mortality events - significantly outperforming existing generic and COVID-19 specific clinical risk scores. CovEWS could enable clinicians to intervene at an earlier stage, and may therefore help in preventing or mitigating COVID-19 related mortality.

Off-policy evaluation in reinforcement learning offers the chance of using observational data to improve future outcomes in domains such as healthcare and education, but safe deployment in high stakes settings requires ways of assessing its validity. Traditional measures such as confidence intervals may be insufficient due to noise, limited data and confounding. In this paper we develop a method that could serve as a hybrid human-AI system, to enable human experts to analyze the validity of policy evaluation estimates. This is accomplished by highlighting observations in the data whose removal will have a large effect on the OPE estimate, and formulating a set of rules for choosing which ones to present to domain experts for validation. We develop methods to compute exactly the influence functions for fitted Q-evaluation with two different function classes: kernel-based and linear least squares, as well as importance sampling methods. Experiments on medical simulations and real-world intensive care unit data demonstrate that our method can be used to identify limitations in the evaluation process and make evaluation more robust., Comment: ICML final version

Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation cannot be formulated analytically. We propose to learn the symmetry transformation with a model consisting of two latent subspaces, where the first subspace captures the target and the second subspace the remaining invariant information. Our approach is based on the deep information bottleneck in combination with a continuous mutual information regulariser. Unlike previous methods, we focus on the challenging task of minimising mutual information in continuous domains. To this end, we base the calculation of mutual information on correlation matrices in combination with a bijective variable transformation. Extensive experiments demonstrate that our model outperforms state-of-the-art methods on artificial and molecular datasets., Comment: Accepted for publication at NeurIPS 2020

Deep models have advanced prediction in many domains, but their lack of interpretability remains a key barrier to the adoption in many real world applications. There exists a large body of work aiming to help humans understand these black box functions to varying levels of granularity -- for example, through distillation, gradients, or adversarial examples. These methods however, all tackle interpretability as a separate process after training. In this work, we take a different approach and explicitly regularize deep models so that they are well-approximated by processes that humans can step-through in little time. Specifically, we train several families of deep neural networks to resemble compact, axis-aligned decision trees without significant compromises in accuracy. The resulting axis-aligned decision functions uniquely make tree regularized models easy for humans to interpret. Moreover, for situations in which a single, global tree is a poor estimator, we introduce a regional tree regularizer that encourages the deep model to resemble a compact, axis-aligned decision tree in predefined, human-interpretable contexts. Using intuitive toy examples as well as medical tasks for patients in critical care and with HIV, we demonstrate that this new family of tree regularizers yield models that are easier for humans to simulate than simpler L1 or L2 penalties without sacrificing predictive power., Comment: arXiv admin note: substantial text overlap with arXiv:1908.04494, arXiv:1711.06178

The lack of interpretability remains a barrier to the adoption of deep neural networks. Recently, tree regularization has been proposed to encourage deep neural networks to resemble compact, axis-aligned decision trees without significant compromises in accuracy. However, it may be unreasonable to expect that a single tree can predict well across all possible inputs. In this work, we propose regional tree regularization, which encourages a deep model to be well-approximated by several separate decision trees specific to predefined regions of the input space. Practitioners can define regions based on domain knowledge of contexts where different decision-making logic is needed. Across many datasets, our approach delivers more accurate predictions than simply training separate decision trees for each region, while producing simpler explanations than other neural net regularization schemes without sacrificing predictive power. Two healthcare case studies in critical care and HIV demonstrate how experts can improve understanding of deep models via our approach., Comment: AAAI 2020 (Oral)

Estimating the causal effects of an intervention in the presence of confounding is a frequently occurring problem in applications such as medicine. The task is challenging since there may be multiple confounding factors, some of which may be missing, and inferences must be made from high-dimensional, noisy measurements. In this paper, we propose a decision-theoretic approach to estimate the causal effects of interventions where a subset of the covariates is unavailable for some patients during testing. Our approach uses the information bottleneck principle to perform a discrete, low-dimensional sufficient reduction of the covariate data to estimate a distribution over confounders. In doing so, we can estimate the causal effect of an intervention where only partial covariate information is available. Our results on a causal inference benchmark and a real application for treating sepsis show that our method achieves state-of-the-art performance, without sacrificing interpretability., Comment: Machine Learning for Health (ML4H) Workshop at NeurIPS 2018 arXiv:1811.07216

Computer vision tasks are difficult because of the large variability in the data that is induced by changes in light, background, partial occlusion as well as the varying pose, texture, and shape of objects. Generative approaches to computer vision allow us to overcome this difficulty by explicitly modeling the physical image formation process. Using generative object models, the analysis of an observed image is performed via Bayesian inference of the posterior distribution. This conceptually simple approach tends to fail in practice because of several difficulties stemming from sampling the posterior distribution: high-dimensionality and multi-modality of the posterior distribution as well as expensive simulation of the rendering process. The main difficulty of sampling approaches in a computer vision context is choosing the proposal distribution accurately so that maxima of the posterior are explored early and the algorithm quickly converges to a valid image interpretation. In this work, we propose to use a Bayesian Neural Network for estimating an image dependent proposal distribution. Compared to a standard Gaussian random walk proposal, this accelerates the sampler in finding regions of the posterior with high value. In this way, we can significantly reduce the number of samples needed to perform facial image analysis., Comment: Accepted to the Bayesian Deep Learning Workshop at NeurIPS 2018

Estimating the causal effects of an intervention from high-dimensional observational data is difficult due to the presence of confounding. The task is often complicated by the fact that we may have a systematic missingness in our data at test time. Our approach uses the information bottleneck to perform a low-dimensional compression of covariates by explicitly considering the relevance of information. Based on the sufficiently reduced covariate, we transfer the relevant information to cases where data is missing at test time, allowing us to reliably and accurately estimate the effects of an intervention, even where data is incomplete. Our results on causal inference benchmarks and a real application for treating sepsis show that our method achieves state-of-the art performance, without sacrificing interpretability.

The lack of interpretability remains a key barrier to the adoption of deep models in many applications. In this work, we explicitly regularize deep models so human users might step through the process behind their predictions in little time. Specifically, we train deep time-series models so their class-probability predictions have high accuracy while being closely modeled by decision trees with few nodes. Using intuitive toy examples as well as medical tasks for treating sepsis and HIV, we demonstrate that this new tree regularization yields models that are easier for humans to simulate than simpler L1 or L2 penalties without sacrificing predictive power., Comment: To appear in AAAI 2018. Contains 9-page main paper and appendix with supplementary material

In this work, we consider the problem of learning a hierarchical generative model of an object from a set of images which show examples of the object in the presence of variable background clutter. Existing approaches to this problem are limited by making strong a-priori assumptions about the object's geometric structure and require segmented training data for learning. In this paper, we propose a novel framework for learning hierarchical compositional models (HCMs) which do not suffer from the mentioned limitations. We present a generalized formulation of HCMs and describe a greedy structure learning framework that consists of two phases: Bottom-up part learning and top-down model composition. Our framework integrates the foreground-background segmentation problem into the structure learning task via a background model. As a result, we can jointly optimize for the number of layers in the hierarchy, the number of parts per layer and a foreground-background segmentation based on class labels only. We show that the learned HCMs are semantically meaningful and achieve competitive results when compared to other generative object models at object classification on a standard transfer learning dataset., Comment: CVPR 2019

This paper considers a Bayesian view for estimating a sub-network in a Markov random field. The sub-network corresponds to the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the posterior such that the Markov blanket is conditionally independent of the network of the potential neighbours. By exploiting this blockwise decoupling, we derive analytic expressions for posterior conditionals. Subsequently, we develop an inference scheme which makes use of the factorization. As a result, estimation of a sub-network is possible without inferring an entire network. Since the resulting Gibbs sampler scales linearly with the number of variables, it can handle relatively large neighbourhoods. The proposed scheme results in faster convergence and superior mixing of the Markov chain than existing Bayesian network estimation techniques., Comment: 16 pages, 5 figures