This paper shows that gradient boosting based on symmetric decision trees can be equivalently reformulated as a kernel method that converges to the solution of a certain Kernel Ridge Regression problem. Thus, we obtain the convergence to a Gaussian Process' posterior mean, which, in turn, allows us to easily transform gradient boosting into a sampler from the posterior to provide better knowledge uncertainty estimates through Monte-Carlo estimation of the posterior variance. We show that the proposed sampler allows for better knowledge uncertainty estimates leading to improved out-of-domain detection.
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The question of whether $Y$ can be predicted based on $X$ often arises and while a well adjusted model may perform well on observed data, the risk of overfitting always exists, leading to poor generalization error on unseen data. This paper proposes a rigorous permutation test to assess the credibility of high $R^2$ values in regression models, which can also be applied to any measure of goodness of fit, without the need for sample splitting, by generating new pairings of $(X_i, Y_j)$ and providing an overall interpretation of the model's accuracy. It introduces a new formulation of the null hypothesis and justification for the test, which distinguishes it from previous literature. The theoretical findings are applied to both simulated data and sensor data of tennis serves in an experimental context. The simulation study underscores how the available information affects the test, showing that the less informative the predictors, the lower the probability of rejecting the null hypothesis, and emphasizing that detecting weaker dependence between variables requires a sufficient sample size.
Model-based approaches to reinforcement learning (MBRL) exhibit favorable performance in practice, but their theoretical guarantees in large spaces are mostly restricted to the setting when transition model is Gaussian or Lipschitz, and demands a posterior estimate whose representational complexity grows unbounded with time. In this work, we develop a novel MBRL method (i) which relaxes the assumptions on the target transition model to belong to a generic family of mixture models; (ii) is applicable to large-scale training by incorporating a compression step such that the posterior estimate consists of a Bayesian coreset of only statistically significant past state-action pairs; and (iii) exhibits a sublinear Bayesian regret. To achieve these results, we adopt an approach based upon Stein's method, which, under a smoothness condition on the constructed posterior and target, allows distributional distance to be evaluated in closed form as the kernelized Stein discrepancy (KSD). The aforementioned compression step is then computed in terms of greedily retaining only those samples which are more than a certain KSD away from the previous model estimate. Experimentally, we observe that this approach is competitive with several state-of-the-art RL methodologies, and can achieve up-to 50 percent reduction in wall clock time in some continuous control environments.
Influence estimation analyzes how changes to the training data can lead to different model predictions; this analysis can help us better understand these predictions, the models making those predictions, and the data sets they're trained on. However, most influence-estimation techniques are designed for deep learning models with continuous parameters. Gradient-boosted decision trees (GBDTs) are a powerful and widely-used class of models; however, these models are black boxes with opaque decision-making processes. In the pursuit of better understanding GBDT predictions and generally improving these models, we adapt recent and popular influence-estimation methods designed for deep learning models to GBDTs. Specifically, we adapt representer-point methods and TracIn, denoting our new methods TREX and BoostIn, respectively; source code is available at //github.com/jjbrophy47/tree_influence. We compare these methods to LeafInfluence and other baselines using 5 different evaluation measures on 22 real-world data sets with 4 popular GBDT implementations. These experiments give us a comprehensive overview of how different approaches to influence estimation work in GBDT models. We find BoostIn is an efficient influence-estimation method for GBDTs that performs equally well or better than existing work while being four orders of magnitude faster. Our evaluation also suggests the gold-standard approach of leave-one-out~(LOO) retraining consistently identifies the single-most influential training example but performs poorly at finding the most influential set of training examples for a given target prediction.
Accurately estimating the probability of failure for safety-critical systems is important for certification. Estimation is often challenging due to high-dimensional input spaces, dangerous test scenarios, and computationally expensive simulators; thus, efficient estimation techniques are important to study. This work reframes the problem of black-box safety validation as a Bayesian optimization problem and introduces an algorithm, Bayesian safety validation, that iteratively fits a probabilistic surrogate model to efficiently predict failures. The algorithm is designed to search for failures, compute the most-likely failure, and estimate the failure probability over an operating domain using importance sampling. We introduce a set of three acquisition functions that focus on reducing uncertainty by covering the design space, optimizing the analytically derived failure boundaries, and sampling the predicted failure regions. Mainly concerned with systems that only output a binary indication of failure, we show that our method also works well in cases where more output information is available. Results show that Bayesian safety validation achieves a better estimate of the probability of failure using orders of magnitude fewer samples and performs well across various safety validation metrics. We demonstrate the algorithm on three test problems with access to ground truth and on a real-world safety-critical subsystem common in autonomous flight: a neural network-based runway detection system. This work is open sourced and currently being used to supplement the FAA certification process of the machine learning components for an autonomous cargo aircraft.
Controller synthesis is in essence a case of model-based planning for non-deterministic environments in which plans (actually ''strategies'') are meant to preserve system goals indefinitely. In the case of supervisory control environments are specified as the parallel composition of state machines and valid strategies are required to be ''non-blocking'' (i.e., always enabling the environment to reach certain marked states) in addition to safe (i.e., keep the system within a safe zone). Recently, On-the-fly Directed Controller Synthesis techniques were proposed to avoid the exploration of the entire -and exponentially large-environment space, at the cost of non-maximal permissiveness, to either find a strategy or conclude that there is none. The incremental exploration of the plant is currently guided by a domain-independent human-designed heuristic. In this work, we propose a new method for obtaining heuristics based on Reinforcement Learning (RL). The synthesis algorithm is thus framed as an RL task with an unbounded action space and a modified version of DQN is used. With a simple and general set of features that abstracts both states and actions, we show that it is possible to learn heuristics on small versions of a problem that generalize to the larger instances, effectively doing zero-shot policy transfer. Our agents learn from scratch in a highly partially observable RL task and outperform the existing heuristic overall, in instances unseen during training.
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems, modeling is much more challenging for stochastic systems in which one is interested in obtaining a predictive distribution over future trajectories. Existing methods are either computationally slow since they rely on Monte Carlo sampling or make simplifying assumptions such that the predictive distribution is unimodal. In this work, we present a deep state-space model which employs graph neural networks in order to model the underlying interacting dynamical system. The predictive distribution is multimodal and has the form of a Gaussian mixture model, where the moments of the Gaussian components can be computed via deterministic moment matching rules. Our moment matching scheme can be exploited for sample-free inference, leading to more efficient and stable training compared to Monte Carlo alternatives. Furthermore, we propose structured approximations to the covariance matrices of the Gaussian components in order to scale up to systems with many agents. We benchmark our novel framework on two challenging autonomous driving datasets. Both confirm the benefits of our method compared to state-of-the-art methods. We further demonstrate the usefulness of our individual contributions in a carefully designed ablation study and provide a detailed runtime analysis of our proposed covariance approximations. Finally, we empirically demonstrate the generalization ability of our method by evaluating its performance on unseen scenarios.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
Existing recommender systems extract the user preference based on learning the correlation in data, such as behavioral correlation in collaborative filtering, feature-feature, or feature-behavior correlation in click-through rate prediction. However, regretfully, the real world is driven by causality rather than correlation, and correlation does not imply causation. For example, the recommender systems can recommend a battery charger to a user after buying a phone, in which the latter can serve as the cause of the former, and such a causal relation cannot be reversed. Recently, to address it, researchers in recommender systems have begun to utilize causal inference to extract causality, enhancing the recommender system. In this survey, we comprehensively review the literature on causal inference-based recommendation. At first, we present the fundamental concepts of both recommendation and causal inference as the basis of later content. We raise the typical issues that the non-causality recommendation is faced. Afterward, we comprehensively review the existing work of causal inference-based recommendation, based on a taxonomy of what kind of problem causal inference addresses. Last, we discuss the open problems in this important research area, along with interesting future works.
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
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