arXiv subjects

Roni Khardon

Publications and source records attributed to Roni Khardon.

At least 19 recordsLinked to original sources

arXiv2025

Learning DNF through Generalized Fourier Representations

The Boolean Fourier representation has been widely used in learning theory, particularly for learning Disjunctive Normal Form (DNF) under uniform and product distributions. Extending these results to non-product distributions has remained a longstanding open problem. We address this challenge by introducing a generalized Fourier representation that enables learning under a broad class of non-product distributions. Our approach represents any distribution $D$ as a Bayesian network (BN) and derives a corresponding Fourier expansion. We show that standard Fourier-based learning techniques using membership queries to identify heavy coefficients can be adapted to this generalized representation with minor modifications. We prove that the $L_1$ spectral norm of conjunctions remains bounded under this expansion for difference-bounded tree BNs, significantly generalizing the known result for uniform distributions; matching lower bounds demonstrate the necessity of these constraints. Using these results, we establish the learnability of DNF and the agnostic learnability of decision trees under such distributions. Finally, we present an algorithm for learning difference-bounded tree BN distributions, extending our results to settings where the distribution is unknown.

cs.DS↗

arXiv2025

Improving planning and MBRL with temporally-extended actions

Continuous time systems are often modeled using discrete time dynamics but this requires a small simulation step to maintain accuracy. In turn, this requires a large planning horizon which leads to computationally demanding planning problems and reduced performance. Previous work in model-free reinforcement learning has partially addressed this issue using action repeats where a policy is learned to determine a discrete action duration. Instead we propose to control the continuous decision timescale directly by using temporally-extended actions and letting the planner treat the duration of the action as an additional optimization variable along with the standard action variables. This additional structure has multiple advantages. It speeds up simulation time of trajectories and, importantly, it allows for deep horizon search in terms of primitive actions while using a shallow search depth in the planner. In addition, in the model-based reinforcement learning (MBRL) setting, it reduces compounding errors from model learning and improves training time for models. We show that this idea is effective and that the range for action durations can be automatically selected using a multi-armed bandit formulation and integrated into the MBRL framework. An extensive experimental evaluation both in planning and in MBRL, shows that our approach yields faster planning, better solutions, and that it enables solutions to problems that are not solved in the standard formulation.

cs.LG↗

arXiv2025

Stability-based Generalization Bounds for Variational Inference

Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly through the connection to PAC-Bayes analysis. A second line of work has provided algorithm-specific generalization bounds through stability arguments or using mutual information bounds, and has shown that the bounds are tight in practice, but unfortunately these bounds do not directly apply to approximate Bayesian algorithms. This paper fills this gap by developing algorithm-specific stability based generalization bounds for a class of approximate Bayesian algorithms that includes VI, specifically when using stochastic gradient descent to optimize their objective. As in the non-Bayesian case, the generalization error is bounded by by expected parameter differences on a perturbed dataset. The new approach complements PAC-Bayes analysis and can provide tighter bounds in some cases. An experimental illustration shows that the new approach yields non-vacuous bounds on modern neural network architectures and datasets and that it can shed light on performance differences between variant approximate Bayesian algorithms.

cs.LG↗

arXiv2024

POAM: Probabilistic Online Attentive Mapping for Efficient Robotic Information Gathering

Gaussian Process (GP) models are widely used for Robotic Information Gathering (RIG) in exploring unknown environments due to their ability to model complex phenomena with non-parametric flexibility and accurately quantify prediction uncertainty. Previous work has developed informative planners and adaptive GP models to enhance the data efficiency of RIG by improving the robot's sampling strategy to focus on informative regions in non-stationary environments. However, computational efficiency becomes a bottleneck when using GP models in large-scale environments with limited computational resources. We propose a framework -- Probabilistic Online Attentive Mapping (POAM) -- that leverages the modeling strengths of the non-stationary Attentive Kernel while achieving constant-time computational complexity for online decision-making. POAM guides the optimization process via variational Expectation Maximization, providing constant-time update rules for inducing inputs, variational parameters, and hyperparameters. Extensive experiments in active bathymetric mapping tasks demonstrate that POAM significantly improves computational efficiency, model accuracy, and uncertainty quantification capability compared to existing online sparse GP models.

cs.RO↗

arXiv2023

Adaptive Robotic Information Gathering via Non-Stationary Gaussian Processes

Robotic Information Gathering (RIG) is a foundational research topic that answers how a robot (team) collects informative data to efficiently build an accurate model of an unknown target function under robot embodiment constraints. RIG has many applications, including but not limited to autonomous exploration and mapping, 3D reconstruction or inspection, search and rescue, and environmental monitoring. A RIG system relies on a probabilistic model's prediction uncertainty to identify critical areas for informative data collection. Gaussian Processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data is typically non-stationary -- different locations do not have the same degree of variability. As a result, the prediction uncertainty does not accurately reveal prediction error, limiting the success of RIG algorithms. We propose a family of non-stationary kernels named Attentive Kernel (AK), which is simple, robust, and can extend any existing kernel to a non-stationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used stationary kernels and the leading non-stationary kernels. The improved uncertainty quantification guides the downstream informative planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with significant spatial variations, enabling the model to characterize salient environmental features.

cs.RO↗

arXiv2023

Variational Inference on the Final-Layer Output of Neural Networks

Traditional neural networks are simple to train but they typically produce overconfident predictions. In contrast, Bayesian neural networks provide good uncertainty quantification but optimizing them is time consuming due to the large parameter space. This paper proposes to combine the advantages of both approaches by performing Variational Inference in the Final layer Output space (VIFO), because the output space is much smaller than the parameter space. We use neural networks to learn the mean and the variance of the probabilistic output. Using the Bayesian formulation we incorporate collapsed variational inference with VIFO which significantly improves the performance in practice. On the other hand, like standard, non-Bayesian models, VIFO enjoys simple training and one can use Rademacher complexity to provide risk bounds for the model. Experiments show that VIFO provides a good tradeoff in terms of run time and uncertainty quantification, especially for out of distribution data.

cs.LG↗

arXiv2023

DiSProD: Differentiable Symbolic Propagation of Distributions for Planning

The paper introduces DiSProD, an online planner developed for environments with probabilistic transitions in continuous state and action spaces. DiSProD builds a symbolic graph that captures the distribution of future trajectories, conditioned on a given policy, using independence assumptions and approximate propagation of distributions. The symbolic graph provides a differentiable representation of the policy's value, enabling efficient gradient-based optimization for long-horizon search. The propagation of approximate distributions can be seen as an aggregation of many trajectories, making it well-suited for dealing with sparse rewards and stochastic environments. An extensive experimental evaluation compares DiSProD to state-of-the-art planners in discrete-time planning and real-time control of robotic systems. The proposed method improves over existing planners in handling stochastic environments, sensitivity to search depth, sparsity of rewards, and large action spaces. Additional real-world experiments demonstrate that DiSProD can control ground vehicles and surface vessels to successfully navigate around obstacles.

cs.RO↗

arXiv2022

On the Performance of Direct Loss Minimization for Bayesian Neural Networks

Direct Loss Minimization (DLM) has been proposed as a pseudo-Bayesian method motivated as regularized loss minimization. Compared to variational inference, it replaces the loss term in the evidence lower bound (ELBO) with the predictive log loss, which is the same loss function used in evaluation. A number of theoretical and empirical results in prior work suggest that DLM can significantly improve over ELBO optimization for some models. However, as we point out in this paper, this is not the case for Bayesian neural networks (BNNs). The paper explores the practical performance of DLM for BNN, the reasons for its failure and its relationship to optimizing the ELBO, uncovering some interesting facts about both algorithms.

cs.LG↗

arXiv2022

Approximate Inference for Stochastic Planning in Factored Spaces

Stochastic planning can be reduced to probabilistic inference in large discrete graphical models, but hardness of inference requires approximation schemes to be used. In this paper we argue that such applications can be disentangled along two dimensions. The first is the direction of information flow in the idealized exact optimization objective, i.e., forward vs backward inference. The second is the type of approximation used to compute this objective, e.g., Belief Propagation (BP) vs mean field variational inference (MFVI). This new categorization allows us to unify a large amount of isolated efforts in prior work explaining their connections and differences as well as potential improvements. An extensive experimental evaluation over large stochastic planning problems shows the advantage of forward BP over several algorithms based on MFVI. An analysis of practical limitations of MFVI motivates a novel algorithm, collapsed state variational inference (CSVI), which provides a tighter approximation and achieves comparable planning performance with forward BP.

cs.AI↗

arXiv2022

Explainable Models via Compression of Tree Ensembles

Ensemble models (bagging and gradient-boosting) of relational decision trees have proved to be one of the most effective learning methods in the area of probabilistic logic models (PLMs). While effective, they lose one of the most important aspect of PLMs -- interpretability. In this paper we consider the problem of compressing a large set of learned trees into a single explainable model. To this effect, we propose CoTE -- Compression of Tree Ensembles -- that produces a single small decision list as a compressed representation. CoTE first converts the trees to decision lists and then performs the combination and compression with the aid of the original training set. An experimental evaluation demonstrates the effectiveness of CoTE in several benchmark relational data sets.

cs.LG↗

arXiv2022

AK: Attentive Kernel for Information Gathering

Robotic Information Gathering (RIG) relies on the uncertainty of a probabilistic model to identify critical areas for efficient data collection. Gaussian processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data typically does not satisfy the assumption of stationarity, where different locations are assumed to have the same degree of variability. As a result, the prediction uncertainty does not accurately capture prediction error, limiting the success of RIG algorithms. We propose a novel family of nonstationary kernels, named the Attentive Kernel (AK), which is simple, robust, and can extend any existing kernel to a nonstationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used RBF kernel and other popular nonstationary kernels. The improved uncertainty quantification guides the downstream RIG planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with high spatial variations, enabling the model to characterize the salient environmental features.

cs.RO↗

arXiv2020

Direct loss minimization algorithms for sparse Gaussian processes

The paper provides a thorough investigation of Direct loss minimization (DLM), which optimizes the posterior to minimize predictive loss, in sparse Gaussian processes. For the conjugate case, we consider DLM for log-loss and DLM for square loss showing a significant performance improvement in both cases. The application of DLM in non-conjugate cases is more complex because the logarithm of expectation in the log-loss DLM objective is often intractable and simple sampling leads to biased estimates of gradients. The paper makes two technical contributions to address this. First, a new method using product sampling is proposed, which gives unbiased estimates of gradients (uPS) for the objective function. Second, a theoretical analysis of biased Monte Carlo estimates (bMC) shows that stochastic gradient descent converges despite the biased gradients. Experiments demonstrate empirical success of DLM. A comparison of the sampling methods shows that, while uPS is potentially more sample-efficient, bMC provides a better tradeoff in terms of convergence time and computational efficiency.

cs.LG↗

arXiv2018

Monte Carlo Structured SVI for Two-Level Non-Conjugate Models

The stochastic variational inference (SVI) paradigm, which combines variational inference, natural gradients, and stochastic updates, was recently proposed for large-scale data analysis in conjugate Bayesian models and demonstrated to be effective in several problems. This paper studies a family of Bayesian latent variable models with two levels of hidden variables but without any conjugacy requirements, making several contributions in this context. The first is observing that SVI, with an improved structured variational approximation, is applicable under more general conditions than previously thought with the only requirement being that the approximating variational distribution be in the same family as the prior. The resulting approach, Monte Carlo Structured SVI (MC-SSVI), significantly extends the scope of SVI, enabling large-scale learning in non-conjugate models. For models with latent Gaussian variables we propose a hybrid algorithm, using both standard and natural gradients, which is shown to improve stability and convergence. Applications in mixed effects models, sparse Gaussian processes, probabilistic matrix factorization and correlated topic models demonstrate the generality of the approach and the advantages of the proposed algorithms.

stat.ML↗

arXiv2017

Stochastic Planning and Lifted Inference

Lifted probabilistic inference (Poole, 2003) and symbolic dynamic programming for lifted stochastic planning (Boutilier et al, 2001) were introduced around the same time as algorithmic efforts to use abstraction in stochastic systems. Over the years, these ideas evolved into two distinct lines of research, each supported by a rich literature. Lifted probabilistic inference focused on efficient arithmetic operations on template-based graphical models under a finite domain assumption while symbolic dynamic programming focused on supporting sequential decision-making in rich quantified logical action models and on open domain reasoning. Given their common motivation but different focal points, both lines of research have yielded highly complementary innovations. In this chapter, we aim to help close the gap between these two research areas by providing an overview of lifted stochastic planning from the perspective of probabilistic inference, showing strong connections to other chapters in this book. This also allows us to define Generalized Lifted Inference as a paradigm that unifies these areas and elucidates open problems for future research that can benefit both lifted inference and stochastic planning.

cs.AI↗

arXiv2015

The Complexity of Reasoning with FODD and GFODD

Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and include numerical values and numerical generalizations of existential and universal quantification. Previous work presented heuristic inference algorithms for GFODDs and implemented these heuristics in systems for decision theoretic planning. In this paper, we study the complexity of the computational problems addressed by such implementations. In particular, we study the evaluation problem, the satisfiability problem, and the equivalence problem for GFODDs under the assumption that the size of the intended model is given with the problem, a restriction that guarantees decidability. Our results provide a complete characterization placing these problems within the polynomial hierarchy. The same characterization applies to the corresponding restriction of problems in first order logic, giving an interesting new avenue for efficient inference when the number of objects is bounded. Our results show that for $Σ_k$ formulas, and for corresponding GFODDs, evaluation and satisfiability are $Σ_k^p$ complete, and equivalence is $Π_{k+1}^p$ complete. For $Π_k$ formulas evaluation is $Π_k^p$ complete, satisfiability is one level higher and is $Σ_{k+1}^p$ complete, and equivalence is $Π_{k+1}^p$ complete.

cs.AI↗

arXiv2014

Probabilistic Relational Planning with First Order Decision Diagrams

Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on symbolic dynamic programming lifted these ideas to first order logic using several representation schemes. Recent work introduced a first order variant of decision diagrams (FODD) and developed a value iteration algorithm for this representation. This paper develops several improvements to the FODD algorithm that make the approach practical. These include, new reduction operators that decrease the size of the representation, several speedup techniques, and techniques for value approximation. Incorporating these, the paper presents a planning system, FODD-Planner, for solving relational stochastic planning problems. The system is evaluated on several domains, including problems from the recent international planning competition, and shows competitive performance with top ranking systems. This is the first demonstration of feasibility of this approach and it shows that abstraction through compact representation is a promising approach to stochastic planning.

cs.AI↗

arXiv2013

Infinite Shift-invariant Grouped Multi-task Learning for Gaussian Processes

Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we develop a novel Bayesian nonparametric model capturing a mixture of Gaussian processes where each task is a sum of a group-specific function and a component capturing individual variation, in addition to each task being phase shifted. We develop an efficient \textsc{em} algorithm to learn the parameters of the model. As a special case we obtain the Gaussian mixture model and \textsc{em} algorithm for phased-shifted periodic time series. Furthermore, we extend the proposed model by using a Dirichlet Process prior and thereby leading to an infinite mixture model that is capable of doing automatic model selection. A Variational Bayesian approach is developed for inference in this model. Experiments in regression, classification and class discovery demonstrate the performance of the proposed models using both synthetic data and real-world time series data from astrophysics. Our methods are particularly useful when the time series are sparsely and non-synchronously sampled.

cs.LG↗

arXiv2013

Online Learning with Pairwise Loss Functions

Efficient online learning with pairwise loss functions is a crucial component in building large-scale learning system that maximizes the area under the Receiver Operator Characteristic (ROC) curve. In this paper we investigate the generalization performance of online learning algorithms with pairwise loss functions. We show that the existing proof techniques for generalization bounds of online algorithms with a univariate loss can not be directly applied to pairwise losses. In this paper, we derive the first result providing data-dependent bounds for the average risk of the sequence of hypotheses generated by an arbitrary online learner in terms of an easily computable statistic, and show how to extract a low risk hypothesis from the sequence. We demonstrate the generality of our results by applying it to two important problems in machine learning. First, we analyze two online algorithms for bipartite ranking; one being a natural extension of the perceptron algorithm and the other using online convex optimization. Secondly, we provide an analysis for the risk bound for an online algorithm for supervised metric learning.

stat.ML↗