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We propose a novel energy-based prior for generative saliency prediction, where the latent variables follow an informative energy-based prior. Both the saliency generator and the energy-based prior are jointly trained via Markov chain Monte Carlo-based maximum likelihood estimation, in which the sampling from the intractable posterior and prior distributions of the latent variables are performed by Langevin dynamics. With the generative saliency model, we can obtain a pixel-wise uncertainty map from an image, indicating model confidence in the saliency prediction. Different from existing generative models, which define the prior distribution of the latent variable as a simple isotropic Gaussian distribution, our model uses an energy-based informative prior which can be more expressive in capturing the latent space of the data. With the informative energy-based prior, we extend the Gaussian distribution assumption of generative models to achieve a more representative distribution of the latent space, leading to more reliable uncertainty estimation. We apply the proposed frameworks to both RGB and RGB-D salient object detection tasks with both transformer and convolutional neural network backbones. Experimental results show that our generative saliency model with an energy-based prior can achieve not only accurate saliency predictions but also reliable uncertainty maps that are consistent with human perception.

Computer models are widely used in decision support for energy systems operation, planning and policy. A system of models is often employed, where model inputs themselves arise from other computer models, with each model being developed by different teams of experts. Gaussian Process emulators can be used to approximate the behaviour of complex, computationally intensive models and used to generate predictions together with a measure of uncertainty about the predicted model output. This paper presents a computationally efficient framework for propagating uncertainty within a network of models with high-dimensional outputs used for energy planning. We present a case study from a UK county council considering low carbon technologies to transform its infrastructure to reach a net-zero carbon target. The system model considered for this case study is simple, however the framework can be applied to larger networks of more complex models.

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through H\"older classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have H\"older densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest.

We present GraphMoE, a novel neural network-based approach to learning generative models for random graphs. The neural network is trained to match the distribution of a class of random graphs by way of a moment estimator. The features used for training are graphlets, subgraph counts of small order. The neural network accepts random noise as input and outputs vector representations for nodes in the graph. Random graphs are then realized by applying a kernel to the representations. Graphs produced this way are demonstrated to be able to imitate data from chemistry, medicine, and social networks. The produced graphs are similar enough to the target data to be able to fool discriminator neural networks otherwise capable of separating classes of random graphs.

One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.

We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on externally provided invariants or templates. We employ algebraic techniques based on linear recurrences and introduce program transformations to simplify probabilistic programs while preserving their statistical properties. We develop power reduction techniques to further simplify the polynomial arithmetic of probabilistic programs and define the theory of moment-computable probabilistic loops for which higher moments can precisely be computed. Our work has applications towards recovering probability distributions of random variables and computing tail probabilities. The empirical evaluation of our results demonstrates the applicability of our work on many challenging examples.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

We present Generative Adversarial Capsule Network (CapsuleGAN), a framework that uses capsule networks (CapsNets) instead of the standard convolutional neural networks (CNNs) as discriminators within the generative adversarial network (GAN) setting, while modeling image data. We provide guidelines for designing CapsNet discriminators and the updated GAN objective function, which incorporates the CapsNet margin loss, for training CapsuleGAN models. We show that CapsuleGAN outperforms convolutional-GAN at modeling image data distribution on the MNIST dataset of handwritten digits, evaluated on the generative adversarial metric and at semi-supervised image classification.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.

Sufficient training data is normally required to train deeply learned models. However, the number of pedestrian images per ID in person re-identification (re-ID) datasets is usually limited, since manually annotations are required for multiple camera views. To produce more data for training deeply learned models, generative adversarial network (GAN) can be leveraged to generate samples for person re-ID. However, the samples generated by vanilla GAN usually do not have labels. So in this paper, we propose a virtual label called Multi-pseudo Regularized Label (MpRL) and assign it to the generated images. With MpRL, the generated samples will be used as supplementary of real training data to train a deep model in a semi-supervised learning fashion. Considering data bias between generated and real samples, MpRL utilizes different contributions from predefined training classes. The contribution-based virtual labels are automatically assigned to generated samples to reduce ambiguous prediction in training. Meanwhile, MpRL only relies on predefined training classes without using extra classes. Furthermore, to reduce over-fitting, a regularized manner is applied to MpRL to regularize the learning process. To verify the effectiveness of MpRL, two state-of-the-art convolutional neural networks (CNNs) are adopted in our experiments. Experiments demonstrate that by assigning MpRL to generated samples, we can further improve the person re-ID performance on three datasets i.e., Market-1501, DukeMTMCreID, and CUHK03. The proposed method obtains +6.29%, +6.30% and +5.58% improvements in rank-1 accuracy over a strong CNN baseline respectively, and outperforms the state-of-the- art methods.