Related papers: A Random Matrix Theory Perspective on the Consiste…

Due to network operation and maintenance relying heavily on network traffic monitoring, traffic matrix analysis has been one of the most crucial issues for network management related tasks. However, it is challenging to reliably obtain the…

It is described how one comes to the Wigner-Dyson random matrix theory (RMT) starting from a model of a disordered metal. The lectures start with a historical introduction where basic ideas of the RMT and theory of disordered metals are…

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…

High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…

Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset…

Purpose: To facilitate the implementation/validation of signal representations and models using parametric matrix-variate distributions to approximate the diffusion tensor distribution (DTD) $\mathcal{P}(\mathbf{D})$. Theory: We establish…

Denoising Diffusion models are gaining increasing popularity in the field of generative modeling for several reasons, including the simple and stable training, the excellent generative quality, and the solid probabilistic foundation. In…

In the field of data mining and machine learning, commonly used classification models cannot effectively learn in unbalanced data. In order to balance the data distribution before model training, oversampling methods are often used to…

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…

Neural networks have been used successfully in a variety of fields, which has led to a great deal of interest in developing a theoretical understanding of how they store the information needed to perform a particular task. We study the…

Diffusion-based generative models demonstrate state-of-the-art performance across various image synthesis tasks, yet their tendency to replicate and amplify dataset biases remains poorly understood. Although previous research has viewed…

The diffusion model has shown remarkable performance in modeling data distributions and synthesizing data. However, the vanilla diffusion model requires complete or fully observed data for training. Incomplete data is a common issue in…

While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing that standard diffusion models trained on natural images…

Standard machine learning is unable to accommodate inputs which do not belong to the training distribution. The resulting models often give rise to confident incorrect predictions which may lead to devastating consequences. This problem is…

Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…

Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into…

Diffusion models generalize well in practice. However, an optimal diffusion model fully memorizes the training data and therefore fails to generalize, raising the question of what induces generalization in a real diffusion model. We show…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory…