Heuristic search solvers like RTDP-Bel and LAO* have proven effective for computing optimal and bounded sub-optimal solutions for Partially Observable Markov Decision Processes (POMDPs), which are typically formulated as belief MDPs. A belief represents a probability distribution over possible system states. Given a parent belief and an action, computing belief state transitions involves Bayesian updates that combine the transition and observation models of the POMDP to determine successor beliefs and their transition probabilities. However, there is a class of problems, specifically in robotics, where computing these transitions can be prohibitively expensive due to costly physics simulations, raycasting, or expensive collision checks required by the underlying transition and observation models, leading to long planning times. To address this challenge, we propose Lazy RTDP-Bel and Lazy LAO*, which defer computing expensive belief state transitions by leveraging Q-value estimation, significantly reducing planning time. We demonstrate the superior performance of the proposed lazy planners in domains such as contact-rich manipulation for pose estimation, outdoor navigation in rough terrain, and indoor navigation with a 1-D LiDAR sensor. Additionally, we discuss practical Q-value estimation techniques for commonly encountered problem classes that our lazy planners can leverage. Our results show that lazy heuristic search methods dramatically improve planning speed by postponing expensive belief transition evaluations while maintaining solution quality.

Weaknesses: The authors neglect to compare to probably the 2 most related works I am aware of. The authors briefly mention variational noise contrastive estimation which can also be used to train models like those presented in this work. While this method has not yet been shown to scale to high dimensional image data it should be used as a comparison for the toy data at the very least. This work: "Variational Inference for Sparse and Undirected Models" Ingraham & Marks provides a method for parameter inference in EBLVMs. This method could also be used for comparison but at the very least should be included in the related work. The proposed method requires 2 inner loop optimizations (N x K) for each model gradient update.

All reviewers agree this is interesting work that succefsully trains energy-based latent variable models with score matching. There were concerns around clarity of the algorithm, utility of latent variables, complexity of the bi-level optimization proess, and missing baselines, which should all be addressed (as promised in the rebuttal) in the final verison of the paper.

Simulation-based inference (SBI) is constantly in search of more expressive and efficient algorithms to accurately infer the parameters of complex simulation models. In line with this goal, we present consistency models for posterior estimation (CMPE), a new conditional sampler for SBI that inherits the advantages of recent unconstrained architectures and overcomes their sampling inefficiency at inference time. CMPE essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture that can be flexibly tailored to the structure of the estimation problem. We provide hyperparameters and default architectures that support consistency training over a wide range of different dimensions, including low-dimensional ones which are important in SBI workflows but were previously difficult to tackle even with unconditional consistency models. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on hard low-dimensional benchmarks, but also achieves competitive performance with much faster sampling speed on two realistic estimation problems with high data and/or parameter dimensions.

It's one paper, cite it as one paper.

The paper shows that profile maximum likelihood, an idea from the distribution estimation literature from a couple of years ago, enjoys optimality properties for a large class of property estimation tasks. The class of tasks includes a number of popular problems studied in the distribution learning literature. All reviewers liked the paper and advocate acceptance. Please do go over the reviews and incorporate any feedback for the camera ready.

Deep neural networks are renowned for their ability to generalise well across diverse tasks, even when heavily overparameterized. Existing works offer only partial explanations (for example, the NTK-based task-model alignment explanation neglects feature learning). Here, we provide an end-to-end, analytically tractable case study that links a network's inductive prior, its training dynamics including feature learning, and its eventual generalisation. Specifically, we exploit the one-to-one correspondence between depth-2 discrete fully connected networks and disjunctive normal form (DNF) formulas by training on Boolean functions. Under a Monte Carlo learning algorithm, our model exhibits predictable training dynamics and the emergence of interpretable features. This framework allows us to trace, in detail, how inductive bias and feature formation drive generalisation.

Kernel method-based intensity estimators, formulated within reproducing kernel Hilbert spaces (RKHSs), and classical kernel intensity estimators (KIEs) have been among the most easy-to-implement and feasible methods for estimating the intensity functions of inhomogeneous Poisson processes. While both approaches share the term "kernel", they are founded on distinct theoretical principles, each with its own strengths and limitations. In this paper, we propose a novel regularized kernel method for Poisson processes based on the least squares loss and show that the resulting intensity estimator involves a specialized variant of the representer theorem: it has the dual coefficient of unity and coincides with classical KIEs. This result provides new theoretical insights into the connection between classical KIEs and kernel method-based intensity estimators, while enabling us to develop an efficient KIE by leveraging advanced techniques from RKHS theory. We refer to the proposed model as the kernel method-based kernel intensity estimator (K$^2$IE). Through experiments on synthetic datasets, we show that K$^2$IE achieves comparable predictive performance while significantly surpassing the state-of-the-art kernel method-based estimator in computational efficiency.

Multimodal contrastive learning is a methodology for linking different data modalities; the canonical example is linking image and text data. The methodology is typically framed as the identification of a set of encoders, one for each modality, that align representations within a common latent space. In this work, we focus on the bimodal setting and interpret contrastive learning as the optimization of (parameterized) encoders that define conditional probability distributions, for each modality conditioned on the other, consistent with the available data. This provides a framework for multimodal algorithms such as crossmodal retrieval, which identifies the mode of one of these conditional distributions, and crossmodal classification, which is similar to retrieval but includes a fine-tuning step to make it task specific. The framework we adopt also gives rise to crossmodal generative models. This probabilistic perspective suggests two natural generalizations of contrastive learning: the introduction of novel probabilistic loss functions, and the use of alternative metrics for measuring alignment in the common latent space. We study these generalizations of the classical approach in the multivariate Gaussian setting. In this context we view the latent space identification as a low-rank matrix approximation problem. This allows us to characterize the capabilities of loss functions and alignment metrics to approximate natural statistics, such as conditional means and covariances; doing so yields novel variants on contrastive learning algorithms for specific mode-seeking and for generative tasks. The framework we introduce is also studied through numerical experiments on multivariate Gaussians, the labeled MNIST dataset, and on a data assimilation application arising in oceanography.

In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution. This general class includes a popular approach that uses a finite element approximation of the stochastic partial differential equation (SPDE) associated with Matérn GP. We explored another scalable alternative popularly used in the computer emulation literature where the basis coefficients at a lattice are drawn from a Gaussian process with an inverse-Gamma bandwidth. For both approaches, we study concentration rates of the posterior distribution. We demonstrated that the SPDE associated approach with a fixed smoothness parameter leads to a suboptimal rate despite how the number of basis functions and bandwidth are chosen when the underlying true function is sufficiently smooth. On the flip side, we showed that the later approach is rate-optimal adaptively over all smoothness levels of the underlying true function if an appropriate prior is placed on the number of basis functions. Efficient computational strategies are developed and numerics are provided to illustrate the theoretical results.