This paper presents a practical and general approach for computing barycentric coordinates through stochastic sampling. Our key insight is a reformulation of the kernel integral defining barycentric coordinates into a weighted least-squares minimization that enables Monte Carlo integration without sacrificing linear precision. Our method can thus compute barycentric coordinates directly at the points of interest, both inside and outside the cage, using just proximity queries to the cage such as closest points and ray intersections. As a result, we can evaluate barycentric coordinates for a large variety of cage representations (from quadrangulated surface meshes to parametric curves) seamlessly, bypassing any volumetric discretization or custom solves. To address the archetypal noise induced by sample-based estimates, we also introduce a denoising scheme tailored to barycentric coordinates. We demonstrate the efficiency and flexibility of our formulation by implementing a stochastic generation of harmonic coordinates, mean-value coordinates, and positive mean-value coordinates.
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We present a practical global error estimation technique for Monte Carlo ray tracing combined with deep learning based denoising. Our method uses aggregated estimates of bias and variance to determine the squared error distribution of the pixels. Unlike unbiased estimates for classical Monte Carlo ray tracing, this distribution follows a noncentral chi-squared distribution, under reasonable assumptions. Based on this, we develop a stopping criterion for denoised Monte Carlo image synthesis that terminates rendering once a user specified error threshold has been achieved. Our results demonstrate that our error estimate and stopping criterion work well on a variety of scenes, and that we are able to achieve a given error threshold without the user specifying the number of samples needed.
In this paper, we propose a novel generative model that utilizes a conditional Energy-Based Model (EBM) for enhancing Variational Autoencoder (VAE), termed Energy-Calibrated VAE (EC-VAE). Specifically, VAEs often suffer from blurry generated samples due to the lack of a tailored training on the samples generated in the generative direction. On the other hand, EBMs can generate high-quality samples but require expensive Markov Chain Monte Carlo (MCMC) sampling. To address these issues, we introduce a conditional EBM for calibrating the generative direction of VAE during training, without requiring it for the generation at test time. In particular, we train EC-VAE upon both the input data and the calibrated samples with adaptive weight to enhance efficacy while avoiding MCMC sampling at test time. Furthermore, we extend the calibration idea of EC-VAE to variational learning and normalizing flows, and apply EC-VAE to an additional application of zero-shot image restoration via neural transport prior and range-null theory. We evaluate the proposed method with two applications, including image generation and zero-shot image restoration, and the experimental results show that our method achieves competitive performance over single-step non-adversarial generation.
FedEvalFair: A Privacy-Preserving and Statistically Grounded Federated Fairness Evaluation Framework
Federated learning has rapidly gained attention in the industrial sector due to its significant advantages in protecting privacy. However, ensuring the fairness of federated learning models post-deployment presents a challenge in practical applications. Given that clients typically rely on limited private datasets to assess model fairness, this constrains their ability to make accurate judgments about the fairness of the model. To address this issue, we propose an innovative evaluation framework, FedEvalFair, which integrates private data from multiple clients to comprehensively assess the fairness of models in actual deployment without compromising data privacy. Firstly, FedEvalFair draws on the concept of federated learning to achieve a comprehensive assessment while protecting privacy. Secondly, based on the statistical concept of "estimating the population from the sample", FedEvalFair is capable of estimating the fairness performance of the model in real-world settings from a limited data sample. Thirdly, we have designed a flexible two-stage evaluation strategy based on statistical hypothesis testing. We verified the theoretical performance and sensitivity to fairness variations of FedEvalFair using Monte Carlo simulations, demonstrating the superior performance of its two-stage evaluation strategy. Additionally, we validated the effectiveness of the FedEvalFair method on real-world datasets, including UCI Adult and eICU, and demonstrated its stability in dealing with real-world data distribution changes compared to traditional evaluation methods.
The fabrication of visual misinformation on the web and social media has increased exponentially with the advent of foundational text-to-image diffusion models. Namely, Stable Diffusion inpainters allow the synthesis of maliciously inpainted images of personal and private figures, and copyrighted contents, also known as deepfakes. To combat such generations, a disruption framework, namely Photoguard, has been proposed, where it adds adversarial noise to the context image to disrupt their inpainting synthesis. While their framework suggested a diffusion-friendly approach, the disruption is not sufficiently strong and it requires a significant amount of GPU and time to immunize the context image. In our work, we re-examine both the minimal and favorable conditions for a successful inpainting disruption, proposing DDD, a “Digression guided Diffusion Disruption” framework. First, we identify the most adversarially vulnerable diffusion timestep range with respect to the hidden space. Within this scope of noised manifold, we pose the problem as a semantic digression optimization. We maximize the distance between the inpainting instance's hidden states and a semantic-aware hidden state centroid, calibrated both by Monte Carlo sampling of hidden states and a discretely projected optimization in the token space. Effectively, our approach achieves stronger disruption and a higher success rate than Photoguard while lowering the GPU memory requirement, and speeding the optimization up to three times faster.
Neural networks often assume independence among input data samples, disregarding correlations arising from inherent clustering patterns in real-world datasets (e.g., due to different sites or repeated measurements). Recently, mixed effects neural networks (MENNs) which separate cluster-specific 'random effects' from cluster-invariant 'fixed effects' have been proposed to improve generalization and interpretability for clustered data. However, existing methods only allow for approximate quantification of cluster effects and are limited to regression and binary targets with only one clustering feature. We present MC-GMENN, a novel approach employing Monte Carlo techniques to train Generalized Mixed Effects Neural Networks. We empirically demonstrate that MC-GMENN outperforms existing mixed effects deep learning models in terms of generalization performance, time complexity, and quantification of inter-cluster variance. Additionally, MC-GMENN is applicable to a wide range of datasets, including multi-class classification tasks with multiple high-cardinality categorical features. For these datasets, we show that MC-GMENN outperforms conventional encoding and embedding methods, simultaneously offering a principled methodology for interpreting the effects of clustering patterns.
Standard approaches for global optimization of non-convex functions, such as branch-and-bound, maintain partition trees to systematically prune the domain. The tree size grows exponentially in the number of dimensions. We propose new sampling-based methods for non-convex optimization that adapts Monte Carlo Tree Search (MCTS) to improve efficiency. Instead of the standard use of visitation count in Upper Confidence Bounds, we utilize numerical overapproximations of the objective as an uncertainty metric, and also take into account of sampled estimates of first-order and second-order information. The Monte Carlo tree in our approach avoids the usual fixed combinatorial patterns in growing the tree, and aggressively zooms into the promising regions, while still balancing exploration and exploitation. We evaluate the proposed algorithms on high-dimensional non-convex optimization benchmarks against competitive baselines and analyze the effects of the hyper parameters.
Bayesian Experimental Design (BED), which aims to find the optimal experimental conditions for Bayesian inference, is usually posed as to optimize the expected information gain (EIG). The gradient information is often needed for efficient EIG optimization, and as a result the ability to estimate the gradient of EIG is essential for BED problems. The primary goal of this work is to develop methods for estimating the gradient of EIG, which, combined with the stochastic gradient descent algorithms, result in efficient optimization of EIG. Specifically, we first introduce a posterior expected representation of the EIG gradient with respect to the design variables. Based on this, we propose two methods for estimating the EIG gradient, UEEG-MCMC that leverages posterior samples generated through Markov Chain Monte Carlo (MCMC) to estimate the EIG gradient, and BEEG-AP that focuses on achieving high simulation efficiency by repeatedly using parameter samples. Theoretical analysis and numerical studies illustrate that UEEG-MCMC is robust agains the actual EIG value, while BEEG-AP is more efficient when the EIG value to be optimized is small. Moreover, both methods show superior performance compared to several popular benchmarks in our numerical experiments.
A Surprisingly Simple Continuous-Action POMDP Solver: Lazy Cross-Entropy Search Over Policy Trees
PDF ↗The Partially Observable Markov Decision Process (POMDP) provides a principled framework for decision making in stochastic partially observable environments. However, computing good solutions for problems with continuous action spaces remains challenging. To ease this challenge, we propose a simple online POMDP solver, called Lazy Cross-Entropy Search Over Policy Trees (LCEOPT). At each planning step, our method uses a novel lazy Cross-Entropy method to search the space of policy trees, which provide a simple policy representation. Specifically, we maintain a distribution on promising finite-horizon policy trees. The distribution is iteratively updated by sampling policies, evaluating them via Monte Carlo simulation, and refitting them to the top-performing ones. Our method is lazy in the sense that it exploits the policy tree representation to avoid redundant computations in policy sampling, evaluation, and distribution update. This leads to computational savings of up to two orders of magnitude. Our LCEOPT is surprisingly simple as compared to existing state-of-the-art methods, yet empirically outperforms them on several continuous-action POMDP problems, particularly for problems with higher-dimensional action spaces.
STAS: Spatial-Temporal Return Decomposition for Solving Sparse Rewards Problems in Multi-agent Reinforcement Learning
PDF ↗Centralized Training with Decentralized Execution (CTDE) has been proven to be an effective paradigm in cooperative multi-agent reinforcement learning (MARL). One of the major challenges is credit assignment, which aims to credit agents by their contributions. They lack the functionality to model complicated relations of the delayed global reward in the temporal dimension and suffer from inefficiencies. To tackle this, we introduce Spatial-Temporal Attention with Shapley (STAS), a novel method that learns credit assignment in both temporal and spatial dimensions. It first decomposes the global return back to each time step, then utilizes the Shapley Value to redistribute the individual payoff from the decomposed global reward. To mitigate the computational complexity of the Shapley Value, we introduce an approximation of marginal contribution and utilize Monte Carlo sampling to estimate it. We evaluate our method on an Alice & Bob example and MPE environments across different scenarios. Our results demonstrate that our method effectively assigns spatial-temporal credit, outperforming all state-of-the-art baselines.
The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian Processes, there has been limited emphasis on the sparse representation of this model. This is mainly due to the increased difficulty in modeling and computation compared to previous sparse Gaussian Processes. Our motivation is to address the need for a sparse representation framework that reduces computational complexity, allowing Student-t Processes to be more flexible for real-world datasets. To achieve this, we leverage the conditional distribution of Student-t Processes to introduce sparse inducing points. Bayesian methods and variational inference are then utilized to derive a well-defined lower bound, facilitating more efficient optimization of our model through stochastic gradient descent. We propose two methods for computing the variational lower bound, one utilizing Monte Carlo sampling and the other employing Jensen's inequality to compute the KL regularization term in the loss function. We propose adopting these approaches as viable alternatives to Gaussian processes when the data might contain outliers or exhibit heavy-tailed behavior, and we provide specific recommendations for their applicability. We evaluate the two proposed approaches on various synthetic and real-world datasets from UCI and Kaggle, demonstrating their effectiveness compared to baseline methods in terms of computational complexity and accuracy, as well as their robustness to outliers.
We investigate the use of a stratified sampling approach for LIME Image, a popular model-agnostic explainable AI method for computer vision tasks, in order to reduce the artifacts generated by typical Monte Carlo sampling. Such artifacts are due to the undersampling of the dependent variable in the synthetic neighborhood around the image being explained, which may result in inadequate explanations due to the impossibility of fitting a linear regressor on the sampled data. We then highlight a connection with the Shapley theory, where similar arguments about undersampling and sample relevance were suggested in the past. We derive all the formulas and adjustment factors required for an unbiased stratified sampling estimator. Experiments show the efficacy of the proposed approach.
Generating high-quality, realistic rendering images for real-time applications generally requires tracing a few samples-per-pixel (spp) and using deep learning-based approaches to denoise the resulting low-spp images. Existing denoising methods necessitate a substantial time expenditure when rendering at high resolutions due to the physically-based sampling and network inference time burdens. In this paper, we propose a novel Monte Carlo sampling strategy to accelerate the sampling process and a corresponding denoiser, subpixel sampling reconstruction (SSR), to obtain high-quality images. Extensive experiments demonstrate that our method significantly outperforms previous approaches in denoising quality and reduces overall time costs, enabling real-time rendering capabilities at 2K resolution.
Model calibration measuring the alignment between the prediction accuracy and model confidence is an important metric reflecting model trustworthiness. Existing dense binary classification methods without proper regularisation of model confidence are prone to being over-confident. To calibrate Deep Neural Networks (DNNs) we propose a Self-Calibrating Vicinal Risk Minimisation (SCVRM) that explores the vicinity space of labeled data where vicinal images that are farther away from labeled images adopt the groundtruth label with decreasing label confidence. We prove that in the logistic regression problem SCVRM can be seen as a Vicinal Risk Minimisation plus a regularisation term that penalises the over-confident predictions. In practical implementation SCVRM is approximated using Monte Carlo sampling that samples additional augmented training images and labels from the vicinal distributions. Experimental results demonstrate that SCVRM can significantly enhance model calibration for different dense classification tasks on both in-distribution and out-of-distribution data. Code is available at https://github.com/Carlisle-Liu/SCVRM.
CGI-DM: Digital Copyright Authentication for Diffusion Models via Contrasting Gradient Inversion
PDF ↗Diffusion Models (DMs) have evolved into advanced image generation tools especially for few-shot generation where a pre-trained model is fine-tuned on a small set of images to capture a specific style or object. Despite their success concerns exist about potential copyright violations stemming from the use of unauthorized data in this process. In response we present Contrasting Gradient Inversion for Diffusion Models (CGI-DM) a novel method featuring vivid visual representations for digital copyright authentication. Our approach involves removing partial information of an image and recovering missing details by exploiting conceptual differences between the pre-trained and fine-tuned models. We formulate the differences as KL divergence between latent variables of the two models when given the same input image which can be maximized through Monte Carlo sampling and Projected Gradient Descent (PGD). The similarity between original and recovered images serves as a strong indicator of potential infringements. Extensive experiments on the WikiArt and Dreambooth datasets demonstrate the high accuracy of CGI-DM in digital copyright authentication surpassing alternative validation techniques. Code implementation is available at https://github.com/Nicholas0228/Revelio.
Deep learning-based methods have achieved significant successes on solving the blind super-resolution (BSR) problem. However most of them request supervised pre-training on labelled datasets. This paper proposes an unsupervised kernel estimation model named dynamic kernel prior (DKP) to realize an unsupervised and pre-training-free learning-based algorithm for solving the BSR problem. DKP can adaptively learn dynamic kernel priors to realize real-time kernel estimation and thereby enables superior HR image restoration performances. This is achieved by a Markov chain Monte Carlo sampling process on random kernel distributions. The learned kernel prior is then assigned to optimize a blur kernel estimation network which entails a network-based Langevin dynamic optimization strategy. These two techniques ensure the accuracy of the kernel estimation. DKP can be easily used to replace the kernel estimation models in the existing methods such as Double-DIP and FKP-DIP or be added to the off-the-shelf image restoration model such as diffusion model. In this paper we incorporate our DKP model with DIP and diffusion model referring to DIP-DKP and Diff-DKP for validations. Extensive simulations on Gaussian and motion kernel scenarios demonstrate that the proposed DKP model can significantly improve the kernel estimation with comparable runtime and memory usage leading to state-of-the-art BSR results. The code is available at https://github.com/XYLGroup/DKP.
One strength of modern language models is their ability to incorporate information from a user-input context when answering queries. However, they are not equally sensitive to the subtle changes to that context.To quantify this, Du et al. (2024) gives an information-theoretic metric to measure such sensitivity. Their metric, susceptibility, is defined as the degree to which contexts can influence a model’s response to a query at a distributional level.However, exactly computing susceptibility is difficult and, thus, Du et al. (2024) falls back on a Monte Carlo approximation.Due to the large number of samples required, the Monte Carlo approximation is inefficient in practice. As a faster alternative, we propose Fisher susceptibility, an efficient method to estimate the susceptibility based on Fisher information.Empirically, we validate that Fisher susceptibility is comparable to Monte Carlo estimated susceptibility across a diverse set of query domains despite its being 70\times faster.Exploiting the improved efficiency, we apply Fisher susceptibility to analyze factors affecting the susceptibility of language models.We observe that larger models are as susceptible as smaller ones.
Computer Vision
While 3D Gaussian Splatting has recently become popular for neural rendering, current methods rely on carefully engineered cloning and splitting strategies for placing Gaussians, which does not always generalize and may lead to poor-quality renderings. For many real-world scenes this leads to their heavy dependence on good initializations. In this work, we rethink the set of 3D Gaussians as a random sample drawn from an underlying probability distribution describing the physical representation of the scene—in other words, Markov Chain Monte Carlo (MCMC) samples. Under this view, we show that the 3D Gaussian updates can be converted as Stochastic Gradient Langevin Dynamics (SGLD) update by simply introducing noise. We then rewrite the densification and pruning strategies in 3D Gaussian Splatting as simply a deterministic state transition of MCMC samples, removing these heuristics from the framework. To do so, we revise the ‘cloning’ of Gaussians into a relocalization scheme that approximately preserves sample probability. To encourage efficient use of Gaussians, we introduce an L1-regularizer on the Gaussians. On various standard evaluation scenes, we show that our method provides improved rendering quality, easy control over the number of Gaussians, and robustness to initialization. The project website is available at https://3dgs-mcmc.github.io/.
Probabilistic Methods · Bayesian Models and Methods
Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC).A common approach is to write the model in a probabilistic programming language and then sample via Hamiltonian Monte Carlo (HMC).However, there are many ways a user can transform a model that make inference more or less efficient.In particular, marginalizing some variables can greatly improve inference but is difficult for users to do manually.We develop an algorithm to easily marginalize random effects in LMMs.A naive approach introduces cubic time operations within an inference algorithm like HMC, but we reduce the running time to linear using fast linear algebra techniques.We show that marginalization is always beneficial when applicable and highlight improvements in various models, especially ones from cognitive sciences.
Reinforcement Learning · Batch Offline
Current approaches to model-based offline reinforcement learning often incorporate uncertainty-based reward penalization to address the distributional shift problem. These approaches, commonly known as pessimistic value iteration, use Monte Carlo sampling to estimate the Bellman target to perform temporal difference-based policy evaluation. We find out that the randomness caused by this sampling step significantly delays convergence. We present a theoretical result demonstrating the strong dependency of suboptimality on the number of Monte Carlo samples taken per Bellman target calculation. Our main contribution is a deterministic approximation to the Bellman target that uses progressive moment matching, a method developed originally for deterministic variational inference. The resulting algorithm, which we call Moment Matching Offline Model-Based Policy Optimization (MOMBO), propagates the uncertainty of the next state through a nonlinear Q-network in a deterministic fashion by approximating the distributions of hidden layer activations by a normal distribution. We show that it is possible to provide tighter guarantees for the suboptimality of MOMBO than the existing Monte Carlo sampling approaches. We also observe MOMBO to converge faster than these approaches in a large set of benchmark tasks.