One major challenge of disentanglement learning with variational autoencoders is the trade-off between disentanglement and reconstruction fidelity. Previous studies, which increase the information bottleneck during training, tend to lose the constraint of disentanglement, leading to the information diffusion problem. In this paper, we present a novel framework for disentangled representation learning, DeVAE, which utilizes hierarchical latent spaces with decreasing information bottlenecks across these spaces. The key innovation of our approach lies in connecting the hierarchical latent spaces through disentanglement-invariant transformations, allowing the sharing of disentanglement properties among spaces while maintaining an acceptable level of reconstruction performance. We demonstrate the effectiveness of DeVAE in achieving a balance between disentanglement and reconstruction through a series of experiments and ablation studies on dSprites and Shapes3D datasets. Code is available at //github.com/erow/disentanglement_lib/tree/pytorch#devae.
相關內容
The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision. In this regard, covariance properties with respect to geometric image transformations in the earliest layers of the visual hierarchy are essential for expressing robust image operations and for formulating invariant visual operations at higher levels. This paper defines and proves a joint covariance property under compositions of spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations, which makes it possible to characterize how different types of image transformations interact with each other. Specifically, the derived relations show how the receptive field parameters need to be transformed, in order to match the output from spatio-temporal receptive fields with the underlying spatio-temporal image transformations.
Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential failure modes of these techniques by rooting popular machine-learning indicators of phase transitions in information-theoretic concepts. Using tools from information geometry, we prove that several machine-learning indicators of phase transitions approximate the square root of the system's (quantum) Fisher information from below -- a quantity that is known to indicate phase transitions but is often difficult to compute from data. We numerically demonstrate the quality of these bounds for phase transitions in classical and quantum systems.
The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision. In this regard, covariance properties with respect to geometric image transformations in the earliest layers of the visual hierarchy are essential for expressing robust image operations and for formulating invariant visual operations at higher levels. This paper defines and proves a joint covariance property under compositions of spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations, which makes it possible to characterize how different types of image transformations interact with each other. Specifically, the derived relations show the receptive field parameters need to be transformed, in order to match the output from spatio-temporal receptive fields with the underlying spatio-temporal image transformations.
Diffusion model has become a main paradigm for synthetic data generation in many subfields of modern machine learning, including computer vision, language model, or speech synthesis. In this paper, we leverage the power of diffusion model for generating synthetic tabular data. The heterogeneous features in tabular data have been main obstacles in tabular data synthesis, and we tackle this problem by employing the auto-encoder architecture. When compared with the state-of-the-art tabular synthesizers, the resulting synthetic tables from our model show nice statistical fidelities to the real data, and perform well in downstream tasks for machine learning utilities. We conducted the experiments over $15$ publicly available datasets. Notably, our model adeptly captures the correlations among features, which has been a long-standing challenge in tabular data synthesis. Our code is available at //github.com/UCLA-Trustworthy-AI-Lab/AutoDiffusion.
Temporal data, obtained in the setting where it is only possible to observe one time point per trajectory, is widely used in different research fields, yet remains insufficiently addressed from the statistical point of view. Such data often contain observations of a large number of entities, in which case it is of interest to identify a small number of representative behavior types. In this paper, we propose a new method performing clustering simultaneously with alignment of temporal objects inferred from these data, providing insight into the relationships between the entities. A series of simulations confirm the ability of the proposed approach to leverage multiple properties of the complex data we target such as accessible uncertainties, correlations and a small number of time points. We illustrate it on real data encoding cellular response to a radiation treatment with high energy, supported with the results of an enrichment analysis.
We study regression adjustment with general function class approximations for estimating the average treatment effect in the design-based setting. Standard regression adjustment involves bias due to sample re-use, and this bias leads to behavior that is sub-optimal in the sample size, and/or imposes restrictive assumptions. Our main contribution is to introduce a novel decorrelation-based approach that circumvents these issues. We prove guarantees, both asymptotic and non-asymptotic, relative to the oracle functions that are targeted by a given regression adjustment procedure. We illustrate our method by applying it to various high-dimensional and non-parametric problems, exhibiting improved sample complexity and weakened assumptions relative to known approaches.
The illness-death model for chronic conditions is combined with a renewal equation for the number of newborns taking into account possibly different fertility rates in the healthy and diseased parts of the population. The resulting boundary value problem consists of a system of partial differential equations with an integral boundary condition. As an application, the boundary value problem is applied to an example about type 2 diabetes.
Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely available. In this chapter, we review theoretically principled unsupervised learning schemes for solving imaging inverse problems, with a particular focus on methods rooted in optimal transport and convex analysis. We begin by reviewing the optimal transport-based unsupervised approaches such as the cycle-consistency-based models and learned adversarial regularization methods, which have clear probabilistic interpretations. Subsequently, we give an overview of a recent line of works on provably convergent learned optimization algorithms applied to accelerate the solution of imaging inverse problems, alongside their dedicated unsupervised training schemes. We also survey a number of provably convergent plug-and-play algorithms (based on gradient-step deep denoisers), which are among the most important and widely applied unsupervised approaches for imaging problems. At the end of this survey, we provide an overview of a few related unsupervised learning frameworks that complement our focused schemes. Together with a detailed survey, we provide an overview of the key mathematical results that underlie the methods reviewed in the chapter to keep our discussion self-contained.
We consider the problem of target detection with a constant false alarm rate (CFAR). This constraint is crucial in many practical applications and is a standard requirement in classical composite hypothesis testing. In settings where classical approaches are computationally expensive or where only data samples are given, machine learning methodologies are advantageous. CFAR is less understood in these settings. To close this gap, we introduce a framework of CFAR constrained detectors. Theoretically, we prove that a CFAR constrained Bayes optimal detector is asymptotically equivalent to the classical generalized likelihood ratio test (GLRT). Practically, we develop a deep learning framework for fitting neural networks that approximate it. Experiments of target detection in different setting demonstrate that the proposed CFARnet allows a flexible tradeoff between CFAR and accuracy.
Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data, existing methods typically rely on a stationary GP assumption for approximation, and can thus perform poorly when the underlying response surface is non-stationary, i.e., it has some regions of rapid change and other regions with little change. Such non-stationarity is, however, ubiquitous in real-world problems, including our motivating application for surrogate modeling of computer experiments. We thus propose a new Product of Sparse GP (ProSpar-GP) method for scalable GP modeling with massive non-stationary data. The ProSpar-GP makes use of a carefully-constructed product-of-experts formulation of sparse GP experts, where different experts are placed within local regions of non-stationarity. These GP experts are fit via a novel variational inference approach, which capitalizes on mini-batching and GPU acceleration for efficient optimization of inducing points and length-scale parameters for each expert. We further show that the ProSpar-GP is Kolmogorov-consistent, in that its generative distribution defines a valid stochastic process over the prediction space; such a property provides essential stability for variational inference, particularly in the presence of non-stationarity. We then demonstrate the improved performance of the ProSpar-GP over the state-of-the-art, in a suite of numerical experiments and an application for surrogate modeling of a satellite drag simulator.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191