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John Paisley

Publications and source records attributed to John Paisley.

At least 55 records · Page 3Linked to original sources
arXiv2025

Bayesian Gaussian Process ODEs via Double Normalizing Flows

Recently, Gaussian processes have been used to model the vector field of continuous dynamical systems, referred to as GPODEs, which are characterized by a probabilistic ODE equation. Bayesian inference for these models has been extensively studied and applied in tasks such as time series prediction. However, the use of standard GPs with basic kernels like squared exponential kernels has been common in GPODE research, limiting the model's ability to represent complex scenarios. To address this limitation, we introduce normalizing flows to reparameterize the ODE vector field, resulting in a data-driven prior distribution, thereby increasing flexibility and expressive power. We develop a data-driven variational learning algorithm that utilizes analytically tractable probability density functions of normalizing flows, enabling simultaneous learning and inference of unknown continuous dynamics. Additionally, we also apply normalizing flows to the posterior inference of GP ODEs to resolve the issue of strong mean-field assumptions in posterior inference. By applying normalizing flows in both these ways, our model improves accuracy and uncertainty estimates for Bayesian Gaussian Process ODEs. We validate the effectiveness of our approach on simulated dynamical systems and real-world human motion data, including time series prediction and missing data recovery tasks. Experimental results show that our proposed method effectively captures model uncertainty while improving accuracy.

cs.LG↗
arXiv2024

Flexible Bayesian Last Layer Models Using Implicit Priors and Diffusion Posterior Sampling

Bayesian Last Layer (BLL) models focus solely on uncertainty in the output layer of neural networks, demonstrating comparable performance to more complex Bayesian models. However, the use of Gaussian priors for last layer weights in Bayesian Last Layer (BLL) models limits their expressive capacity when faced with non-Gaussian, outlier-rich, or high-dimensional datasets. To address this shortfall, we introduce a novel approach that combines diffusion techniques and implicit priors for variational learning of Bayesian last layer weights. This method leverages implicit distributions for modeling weight priors in BLL, coupled with diffusion samplers for approximating true posterior predictions, thereby establishing a comprehensive Bayesian prior and posterior estimation strategy. By delivering an explicit and computationally efficient variational lower bound, our method aims to augment the expressive abilities of BLL models, enhancing model accuracy, calibration, and out-of-distribution detection proficiency. Through detailed exploration and experimental validation, We showcase the method's potential for improving predictive accuracy and uncertainty quantification while ensuring computational efficiency.

cs.LG↗
arXiv2024

Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inference

Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to reduce computational complexity and improve model efficiency. However, inferring the posterior distribution of inducing points is not straightforward. Traditional variational inference approaches to posterior approximation often lead to significant bias. To address this issue, we propose an alternative method called Denoising Diffusion Variational Inference (DDVI) that uses a denoising diffusion stochastic differential equation (SDE) to generate posterior samples of inducing variables. We rely on score matching methods for denoising diffusion model to approximate score functions with a neural network. Furthermore, by combining classical mathematical theory of SDEs with the minimization of KL divergence between the approximate and true processes, we propose a novel explicit variational lower bound for the marginal likelihood function of DGP. Through experiments on various datasets and comparisons with baseline methods, we empirically demonstrate the effectiveness of DDVI for posterior inference of inducing points for DGP models.

cs.LG↗
arXiv2024

Scalable Community Detection in Massive Networks Using Aggregated Relational Data

The mixed membership stochastic blockmodel (MMSB) is a popular Bayesian network model for community detection. Fitting such large Bayesian network models quickly becomes computationally infeasible when the number of nodes grows into hundreds of thousands and millions. In this paper we propose a novel mini-batch strategy based on aggregated relational data that leverages nodal information to fit MMSB to massive networks. We describe a scalable inference method that can utilize nodal information that often accompanies real-world networks. Conditioning on this extra information leads to a model that admits a parallel stochastic variational inference algorithm, utilizing stochastic gradients of bipartite graph formed from aggregated network ties between node subpopulations. We apply our method to a citation network with over two million nodes and 25 million edges, capturing explainable structure in this network. Our method recovers parameters and achieves better convergence on simulated networks generated according to the MMSB.

cs.SI↗
arXiv2024

Gaussian Process Neural Additive Models

Deep neural networks have revolutionized many fields, but their black-box nature also occasionally prevents their wider adoption in fields such as healthcare and finance, where interpretable and explainable models are required. The recent development of Neural Additive Models (NAMs) is a significant step in the direction of interpretable deep learning for tabular datasets. In this paper, we propose a new subclass of NAMs that use a single-layer neural network construction of the Gaussian process via random Fourier features, which we call Gaussian Process Neural Additive Models (GP-NAM). GP-NAMs have the advantage of a convex objective function and number of trainable parameters that grows linearly with feature dimensionality. It suffers no loss in performance compared to deeper NAM approaches because GPs are well-suited for learning complex non-parametric univariate functions. We demonstrate the performance of GP-NAM on several tabular datasets, showing that it achieves comparable or better performance in both classification and regression tasks with a large reduction in the number of parameters.

cs.LG↗
arXiv2023

Bayesian Beta-Bernoulli Process Sparse Coding with Deep Neural Networks

Several approximate inference methods have been proposed for deep discrete latent variable models. However, non-parametric methods which have previously been successfully employed for classical sparse coding models have largely been unexplored in the context of deep models. We propose a non-parametric iterative algorithm for learning discrete latent representations in such deep models. Additionally, to learn scale invariant discrete features, we propose local data scaling variables. Lastly, to encourage sparsity in our representations, we propose a Beta-Bernoulli process prior on the latent factors. We evaluate our spare coding model coupled with different likelihood models. We evaluate our method across datasets with varying characteristics and compare our results to current amortized approximate inference methods.

cs.LG↗
arXiv2023

Nonlinear Kalman Filtering with Reparametrization Gradients

We introduce a novel nonlinear Kalman filter that utilizes reparametrization gradients. The widely used parametric approximation is based on a jointly Gaussian assumption of the state-space model, which is in turn equivalent to minimizing an approximation to the Kullback-Leibler divergence. It is possible to obtain better approximations using the alpha divergence, but the resulting problem is substantially more complex. In this paper, we introduce an alternate formulation based on an energy function, which can be optimized instead of the alpha divergence. The optimization can be carried out using reparametrization gradients, a technique that has recently been utilized in a number of deep learning models.

cs.LG↗
arXiv2021

Self-Verification in Image Denoising

We devise a new regularization, called self-verification, for image denoising. This regularization is formulated using a deep image prior learned by the network, rather than a traditional predefined prior. Specifically, we treat the output of the network as a ``prior'' that we denoise again after ``re-noising''. The comparison between the again denoised image and its prior can be interpreted as a self-verification of the network's denoising ability. We demonstrate that self-verification encourages the network to capture low-level image statistics needed to restore the image. Based on this self-verification regularization, we further show that the network can learn to denoise even if it has not seen any clean images. This learning strategy is self-supervised, and we refer to it as Self-Verification Image Denoising (SVID). SVID can be seen as a mixture of learning-based methods and traditional model-based denoising methods, in which regularization is adaptively formulated using the output of the network. We show the application of SVID to various denoising tasks using only observed corrupted data. It can achieve the denoising performance close to supervised CNNs.

eess.IV↗
arXiv2021

Bayesian non-parametric non-negative matrix factorization for pattern identification in environmental mixtures

Environmental health researchers may aim to identify exposure patterns that represent sources, product use, or behaviors that give rise to mixtures of potentially harmful environmental chemical exposures. We present Bayesian non-parametric non-negative matrix factorization (BN^2MF) as a novel method to identify patterns of chemical exposures when the number of patterns is not known a priori. We placed non-negative continuous priors on pattern loadings and individual scores to enhance interpretability and used a clever non-parametric sparse prior to estimate the pattern number. We further derived variational confidence intervals around estimates; this is a critical development because it quantifies the model's confidence in estimated patterns. These unique features contrast with existing pattern recognition methods employed in this field which are limited by user-specified pattern number, lack of interpretability of patterns in terms of human understanding, and lack of uncertainty quantification.

stat.ME↗
arXiv2020

Adaptive noise imitation for image denoising

The effectiveness of existing denoising algorithms typically relies on accurate pre-defined noise statistics or plenty of paired data, which limits their practicality. In this work, we focus on denoising in the more common case where noise statistics and paired data are unavailable. Considering that denoising CNNs require supervision, we develop a new \textbf{adaptive noise imitation (ADANI)} algorithm that can synthesize noisy data from naturally noisy images. To produce realistic noise, a noise generator takes unpaired noisy/clean images as input, where the noisy image is a guide for noise generation. By imposing explicit constraints on the type, level and gradient of noise, the output noise of ADANI will be similar to the guided noise, while keeping the original clean background of the image. Coupling the noisy data output from ADANI with the corresponding ground-truth, a denoising CNN is then trained in a fully-supervised manner. Experiments show that the noisy data produced by ADANI are visually and statistically similar to real ones so that the denoising CNN in our method is competitive to other networks trained with external paired data.

eess.IV↗
arXiv2020

Bayesian recurrent state space model for rs-fMRI

We propose a hierarchical Bayesian recurrent state space model for modeling switching network connectivity in resting state fMRI data. Our model allows us to uncover shared network patterns across disease conditions. We evaluate our method on the ADNI2 dataset by inferring latent state patterns corresponding to altered neural circuits in individuals with Mild Cognitive Impairment (MCI). In addition to states shared across healthy and individuals with MCI, we discover latent states that are predominantly observed in individuals with MCI. Our model outperforms current state of the art deep learning method on ADNI2 dataset.

stat.ML↗
arXiv2020

Deep Bayesian Nonparametric Factor Analysis

We propose a deep generative factor analysis model with beta process prior that can approximate complex non-factorial distributions over the latent codes. We outline a stochastic EM algorithm for scalable inference in a specific instantiation of this model and present some preliminary results.

stat.ML↗
arXiv2020

Noise2Blur: Online Noise Extraction and Denoising

We propose a new framework called Noise2Blur (N2B) for training robust image denoising models without pre-collected paired noisy/clean images. The training of the model requires only some (or even one) noisy images, some random unpaired clean images, and noise-free but blurred labels obtained by predefined filtering of the noisy images. The N2B model consists of two parts: a denoising network and a noise extraction network. First, the noise extraction network learns to output a noise map using the noise information from the denoising network under the guidence of the blurred labels. Then, the noise map is added to a clean image to generate a new "noisy/clean" image pair. Using the new image pair, the denoising network learns to generate clean and high-quality images from noisy observations. These two networks are trained simultaneously and mutually aid each other to learn the mappings of noise to clean/blur. Experiments on several denoising tasks show that the denoising performance of N2B is close to that of other denoising CNNs trained with pre-collected paired data.

eess.IV↗
arXiv2020

Ro-SOS: Metric Expression Network (MEnet) for Robust Salient Object Segmentation

Although deep CNNs have brought significant improvement to image saliency detection, most CNN based models are sensitive to distortion such as compression and noise. In this paper, we propose an end-to-end generic salient object segmentation model called Metric Expression Network (MEnet) to deal with saliency detection with the tolerance of distortion. Within MEnet, a new topological metric space is constructed, whose implicit metric is determined by the deep network. As a result, we manage to group all the pixels in the observed image semantically within this latent space into two regions: a salient region and a non-salient region. With this architecture, all feature extractions are carried out at the pixel level, enabling fine granularity of output boundaries of the salient objects. What's more, we try to give a general analysis for the noise robustness of the network in the sense of Lipschitz and Jacobian literature. Experiments demonstrate that robust salient maps facilitating object segmentation can be generated by the proposed metric. Tests on several public benchmarks show that MEnet has achieved desirable performance. Furthermore, by direct computation and measuring the robustness, the proposed method outperforms previous CNN-based methods on distorted inputs.

cs.CV↗
arXiv2019

Learning Rate Dropout

The performance of a deep neural network is highly dependent on its training, and finding better local optimal solutions is the goal of many optimization algorithms. However, existing optimization algorithms show a preference for descent paths that converge slowly and do not seek to avoid bad local optima. In this work, we propose Learning Rate Dropout (LRD), a simple gradient descent technique for training related to coordinate descent. LRD empirically aids the optimizer to actively explore in the parameter space by randomly setting some learning rates to zero; at each iteration, only parameters whose learning rate is not 0 are updated. As the learning rate of different parameters is dropped, the optimizer will sample a new loss descent path for the current update. The uncertainty of the descent path helps the model avoid saddle points and bad local minima. Experiments show that LRD is surprisingly effective in accelerating training while preventing overfitting.

cs.CV↗
arXiv2019

Risk Bounds for Low Cost Bipartite Ranking

Bipartite ranking is an important supervised learning problem; however, unlike regression or classification, it has a quadratic dependence on the number of samples. To circumvent the prohibitive sample cost, many recent work focus on stochastic gradient-based methods. In this paper we consider an alternative approach, which leverages the structure of the widely-adopted pairwise squared loss, to obtain a stochastic and low cost algorithm that does not require stochastic gradients or learning rates. Using a novel uniform risk bound---based on matrix and vector concentration inequalities---we show that the sample size required for competitive performance against the all-pairs batch algorithm does not have a quadratic dependence. Generalization bounds for both the batch and low cost stochastic algorithms are presented. Experimental results show significant speed gain against the batch algorithm, as well as competitive performance against state-of-the-art bipartite ranking algorithms on real datasets.

cs.LG↗
arXiv2019

Accurate Uncertainty Estimation and Decomposition in Ensemble Learning

Ensemble learning is a standard approach to building machine learning systems that capture complex phenomena in real-world data. An important aspect of these systems is the complete and valid quantification of model uncertainty. We introduce a Bayesian nonparametric ensemble (BNE) approach that augments an existing ensemble model to account for different sources of model uncertainty. BNE augments a model's prediction and distribution functions using Bayesian nonparametric machinery. It has a theoretical guarantee in that it robustly estimates the uncertainty patterns in the data distribution, and can decompose its overall predictive uncertainty into distinct components that are due to different sources of noise and error. We show that our method achieves accurate uncertainty estimates under complex observational noise, and illustrate its real-world utility in terms of uncertainty decomposition and model bias detection for an ensemble in predict air pollution exposures in Eastern Massachusetts, USA.

cs.LG↗
arXiv2019

Reweighted Expectation Maximization

Training deep generative models with maximum likelihood remains a challenge. The typical workaround is to use variational inference (VI) and maximize a lower bound to the log marginal likelihood of the data. Variational auto-encoders (VAEs) adopt this approach. They further amortize the cost of inference by using a recognition network to parameterize the variational family. Amortized VI scales approximate posterior inference in deep generative models to large datasets. However it introduces an amortization gap and leads to approximate posteriors of reduced expressivity due to the problem known as posterior collapse. In this paper, we consider expectation maximization (EM) as a paradigm for fitting deep generative models. Unlike VI, EM directly maximizes the log marginal likelihood of the data. We rediscover the importance weighted auto-encoder (IWAE) as an instance of EM and propose a new EM-based algorithm for fitting deep generative models called reweighted expectation maximization (REM). REM learns better generative models than the IWAE by decoupling the learning dynamics of the generative model and the recognition network using a separate expressive proposal found by moment matching. We compared REM to the VAE and the IWAE on several density estimation benchmarks and found it leads to significantly better performance as measured by log-likelihood.

stat.ML↗