Predicting and anticipating future outcomes or reasoning about missing information in a sequence are critical skills for agents to be able to make intelligent decisions. This requires strong, temporally coherent generative capabilities. Diffusion models have shown remarkable success in several generative tasks, but have not been extensively explored in the video domain. We present Random-Mask Video Diffusion (RaMViD), which extends image diffusion models to videos using 3D convolutions, and introduces a new conditioning technique during training. By varying the mask we condition on, the model is able to perform video prediction, infilling, and upsampling. Due to our simple conditioning scheme, we can utilize the same architecture as used for unconditional training, which allows us to train the model in a conditional and unconditional fashion at the same time. We evaluate RaMViD on two benchmark datasets for video prediction, on which we achieve state-of-the-art results, and one for video generation. High-resolution videos are provided at https://sites.google.com/view/video-diffusion-prediction.

Denoising diffusion probabilistic models (DDPM) are powerful hierarchical latent variable models with remarkable sample generation quality and training stability. These properties can be attributed to parameter sharing in the generative hierarchy, as well as a parameter-free diffusion-based inference procedure. In this paper, we present Few-Shot Diffusion Models (FSDM), a framework for few-shot generation leveraging conditional DDPMs. FSDMs are trained to adapt the generative process conditioned on a small set of images from a given class by aggregating image patch information using a set-based Vision Transformer (ViT). At test time, the model is able to generate samples from previously unseen classes conditioned on as few as 5 samples from that class. We empirically show that FSDM can perform few-shot generation and transfer to new datasets. We benchmark variants of our method on complex vision datasets for few-shot learning and compare to unconditional and conditional DDPM baselines. Additionally, we show how conditioning the model on patch-based input set information improves training convergence.

Generative flows and diffusion models have been predominantly trained on ordinal data, for example natural images. This paper introduces two extensions of flows and diffusion for categorical data such as language or image segmentation: Argmax Flows and Multinomial Diffusion. Argmax Flows are defined by a composition of a continuous distribution (such as a normalizing flow), and an argmax function. To optimize this model, we learn a probabilistic inverse for the argmax that lifts the categorical data to a continuous space. Multinomial Diffusion gradually adds categorical noise in a diffusion process, for which the generative denoising process is learned. We demonstrate that our method outperforms existing dequantization approaches on text modelling and modelling on image segmentation maps in log-likelihood.

This paper introduces a new method to define and train continuous distributions such as normalizing flows directly on categorical data, for example text and image segmentation. The generative model is defined by a composition of a normalizing flow and an argmax function. To optimize this model, we dequantize the argmax using a distribution that is a probabilistic right-inverse to the argmax. This distribution lifts the categorical data to a continuous space on which the flow can be trained. We demonstrate that applying existing dequantization techniques na¨ıvely to categorical data leads to suboptimal solutions. In addition, the model is fast both in generative (for sampling) and inference direction (for training), as opposed to autoregressive models.

Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. However, a major limitation of HMC is its inability to be applied to discrete domains due to the lack of gradient signal. In this work, we introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions using a combination of neural transport methods like normalizing flows and variational dequantization, and the Metropolis-Hastings rule. Our method first learns a continuous embedding of the discrete space using a surjective map and subsequently learns a bijective transformation from the continuous space to an approximately Gaussian distributed latent variable. Sampling proceeds by simulating MCMC chains in the latent space and mapping these samples to the target discrete space via the learned transformations. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.

Flow models have recently made great progress at modeling ordinal discrete data such as images and audio. Due to the continuous nature of flow models, dequantization is typically applied when using them for such discrete data, resulting in lower bound estimates of the likelihood. In this paper, we introduce subset flows , a class of flows that can tractably transform finite volumes and thus allow exact computation of likelihoods for discrete data. Based on subset flows, we identify ordinal discrete autoregressive models, including WaveNets, PixelCNNs and Transformers, as single-layer flows. We use the flow formulation to compare models trained and evaluated with either the exact likelihood or its dequantization lower bound. Finally, we study multilayer flows composed of PixelCNNs and non-autoregressive coupling layers and demonstrate state-of-the-art results on CIFAR-10 for flow models trained with dequantization.

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model densities whereas VAEs learn stochastic transformations that are non-invertible and thus typically do not provide tractable estimates of the marginal likelihood. In this paper, we introduce SurVAE Flows: A modular framework of composable transformations that encompasses VAEs and normalizing flows. SurVAE Flows bridge the gap between normalizing flows and VAEs with surjective transformations , wherein the transformations are deterministic in one direction - thereby allowing exact likelihood computation, and stochastic in the reverse direction - hence providing a lower bound on the corresponding likelihood. We show that several recently proposed methods, including dequantization and augmented normalizing flows, can be expressed as SurVAE Flows. Finally, we introduce common operations such as the max value , the absolute value, sorting and stochastic permutation as composable layers in SurVAE Flows.

Flow models have recently made great progress at modelling sensor data such as images, audio, etc., but are still outperformed by autoregressive models. We present a novel interpretation of several existing autoregressive models, including WaveNet, PixelCNN and PixelCNN++, as single-layer flow models defined through an invertible transformation between uniform noise and data samples. These models thus admit a latent representation of data. To demonstrate the usefulness of this interpretation, we explore the latent space of PixelCNN and PixelCNN++ by inspecting latent image representations and performing latent space interpolations.

Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a diagonal approximation of the covariance matrix despite the fact that these matrices are known to result in poor uncertainty estimates. To address this issue, we propose a new stochastic, low-rank, approximate natural-gradient (SLANG) method for variational inference in large, deep models. Our method estimates a "diagonal plus low-rank" structure based solely on back-propagated gradients of the network log-likelihood. This requires strictly less gradient computations than methods that compute the gradient of the whole variational objective. Empirical evaluations on standard benchmarks confirm that SLANG enables faster and more accurate estimation of uncertainty than mean-field methods, and performs comparably to state-of-the-art methods.

Uncertainty computation in deep learning is essential to design robust and reliable systems. Variational inference (VI) is a promising approach for such computation, but requires more effort to implement and execute compared to maximum-likelihood methods. In this paper, we propose new natural-gradient algorithms to reduce such efforts for Gaussian mean-field VI. Our algorithms can be implemented within the Adam optimizer by perturbing the network weights during gradient evaluations, and uncertainty estimates can be cheaply obtained by using the vector that adapts the learning rate. This requires lower memory, computation, and implementation effort than existing VI methods, while obtaining uncertainty estimates of comparable quality. Our empirical results confirm this and further suggest that the weight-perturbation in our algorithm could be useful for exploration in reinforcement learning and stochastic optimization.

Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating Bayesian inference as an optimization problem and solving it using gradient-based optimization. In this paper, we argue in favor of natural-gradient approaches which, unlike their gradientbased counterparts, can improve convergence by exploiting the information geometry of the solutions. We show how to derive fast yet simple natural-gradient updates by using a duality associated with exponential-family distributions. An attractive feature of these methods is that, by using natural-gradients, they are able to extract accurate local approximations for individual model components. We summarize recent results for Bayesian deep learning showing the superiority of natural-gradient approaches over their gradient counterparts.

We present the Variational Adaptive Newton (VAN) method which is a black-box optimization method especially suitable for explorative-learning tasks such as active learning and reinforcement learning. Similar to Bayesian methods, VAN estimates a distribution that can be used for exploration, but requires computations that are similar to continuous optimization methods. Our theoretical contribution reveals that VAN is a second-order method that unifies existing methods in distinct fields of continuous optimization, variational inference, and evolution strategies. Our experimental results show that VAN performs well on a wide-variety of learning tasks. This work presents a general-purpose explorative-learning method that has the potential to improve learning in areas such as active learning and reinforcement learning.

We propose a new method for amortized inference in graphical models that contain deep generative models. Our method generalizes existing approaches to a larger class of models where the graphical model can contain non-conjugate components. Our main contribution is the proposal of structured recognition models that preserve the correlations between all local variables. For this general class of models, we derive a scalable inference method that employs natural-gradient updates and can be implemented by reusing existing software for graphical models and deep models.

Tree boosting has empirically proven to be a highly effective approach to predictive modeling. It has shown remarkable results for a vast array of problems. For many years, MART has been the tree boosting method of choice. More recently, a tree boosting method known as XGBoost has gained popularity by winning numerous machine learning competitions. In this thesis, we will investigate how XGBoost differs from the more traditional MART. We will show that XGBoost employs a boosting algorithm which we will term Newton boosting. This boosting algorithm will further be compared with the gradient boosting algorithm that MART employs. Moreover, we will discuss the regularization techniques that these methods offer and the effect these have on the models. In addition to this, we will attempt to answer the question of why XGBoost seems to win so many competitions. To do this, we will provide some arguments for why tree boosting, and in particular XGBoost, seems to be such a highly effective and versatile approach to predictive modeling. The core argument is that tree boosting can be seen to adaptively determine the local neighbourhoods of the model. Tree boosting can thus be seen to take the bias-variance tradeoff into consideration during model fitting. XGBoost further introduces some subtle improvements which allows it to deal with the bias-variance tradeoff even more carefully.

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model densities whereas VAEs learn stochastic transformations that are non-invertible and thus typically do not provide tractable estimates of the marginal likelihood. In this paper, we introduce SurVAE Flows: A modular framework of composable transformations that encompasses VAEs and normalizing flows. SurVAE Flows bridge the gap between normalizing flows and VAEs with surjective transformations , wherein the transformations are deterministic in one direction – thereby allowing exact likelihood computation, and stochastic in the reverse direction – hence providing a lower bound on the corresponding likelihood. We show that several recently proposed methods, including dequantization and augmented normalizing flows, can be expressed as SurVAE Flows. Finally, we introduce common operations such as the max value , the absolute value , sorting and stochastic permutation as composable layers in SurVAE Flows.