The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions. However, prior analyses of this framework have primarily focused on the continuous-time setting, assuming a perfect solution of the underlying equations. In this work, we present the first discrete-time analysis of the stochastic interpolant framework, where we introduce an innovative discrete-time sampler and derive a finite-time upper bound on its distribution estimation error. Our result provides a novel quantification of how different factors, including the distance between source and target distributions and estimation accuracy, affect the convergence rate and also offers a new principled way to design efficient schedules for convergence acceleration. Finally, numerical experiments are conducted on the discrete-time sampler to corroborate our theoretical findings.

Random feature latent variable models (RFLVMs) represent the state-of-the-art in latent variable models, capable of handling non-Gaussian likelihoods and effectively uncovering patterns in high-dimensional data. However, their heavy reliance on Monte Carlo sampling results in scalability issues which makes it difficult to use these models for datasets with a massive number of observations. To scale up RFLVMs, we turn to the optimization-based variational Bayesian inference (VBI) algorithm which is known for its scalability compared to sampling-based methods. However, implementing VBI for RFLVMs poses challenges, such as the lack of explicit probability distribution functions (PDFs) for the Dirichlet process (DP) in the kernel learning component, and the incompatibility of existing VBI algorithms with RFLVMs. To address these issues, we introduce a stick-breaking construction for DP to obtain an explicit PDF and a novel VBI algorithm called ``block coordinate descent variational inference" (BCD-VI). This enables the development of a scalable version of RFLVMs, or in short, SRFLVM. Our proposed method shows scalability, computational efficiency, superior performance in generating informative latent representations and the ability of imputing missing data across various real-world datasets, outperforming state-of-the-art competitors.

Understanding local risks from extreme rainfall, such as flooding, requires both long records (to sample rare events) and high-resolution products (to assess localized hazards). Unfortunately, there is a dearth of long-record and high-resolution products that can be used to understand local risk and precipitation science. In this paper, we present a novel generative diffusion model that downscales (super-resolves) globally available Climate Prediction Center (CPC) gauge-based precipitation products and ERA5 reanalysis data to generate kilometer-scale precipitation estimates. Downscaling gauge-based precipitation from 55 km to 1 km while recovering extreme rainfall signals poses significant challenges. To enforce our model (named WassDiff) to produce well-calibrated precipitation intensity values, we introduce a Wasserstein Distance Regularization (WDR) term for the score-matching training objective in the diffusion denoising process. We show that WDR greatly enhances the model's ability to capture extreme values compared to diffusion without WDR. Extensive evaluation shows that WassDiff has better reconstruction accuracy and bias scores than conventional score-based diffusion models. Case studies of extreme weather phenomena, like tropical storms and cold fronts, demonstrate WassDiff's ability to produce appropriate spatial patterns while capturing extremes. Such downscaling capability enables the generation of extensive km-scale precipitation datasets from existing historical global gauge records and current gauge measurements in areas without high-resolution radar.

Data-driven intelligent computational design (DICD) is a research hotspot emerged under the context of fast-developing artificial intelligence. It emphasizes on utilizing deep learning algorithms to extract and represent the design features hidden in historical or fabricated design process data, and then learn the combination and mapping patterns of these design features for the purposes of design solution retrieval, generation, optimization, evaluation, etc. Due to its capability of automatically and efficiently generating design solutions and thus supporting human-in-the-loop intelligent and innovative design activities, DICD has drawn the attentions from both academic and industrial fields. However, as an emerging research subject, there are still many unexplored issues that limit the development and application of DICD, such as specific dataset building, engineering design related feature engineering, systematic methods and techniques for DICD implementation in the entire product design process, etc. In this regard, a systematic and operable road map for DICD implementation from full-process perspective is established, including a general workflow for DICD project planning, an overall framework for DICD project implementation, the computing mechanisms for DICD implementation, key enabling technologies for detailed DICD implementation, and three application scenarios of DICD. The road map reveals the common mechanisms and calculation principles of existing DICD researches, and thus it can provide systematic guidance for the possible DICD applications that have not been explored.

In this paper, we present a Neural Preset technique to address the limitations of existing color style transfer methods, including visual artifacts, vast memory requirement, and slow style switching speed. Our method is based on two core designs. First, we propose Deterministic Neural Color Mapping (DNCM) to consistently operate on each pixel via an image-adaptive color mapping matrix, avoiding artifacts and supporting high-resolution inputs with a small memory footprint. Second, we develop a two-stage pipeline by dividing the task into color normalization and stylization, which allows efficient style switching by extracting color styles as presets and reusing them on normalized input images. Due to the unavailability of pairwise datasets, we describe how to train Neural Preset via a self-supervised strategy. Various advantages of Neural Preset over existing methods are demonstrated through comprehensive evaluations. Notably, Neural Preset enables stable 4K color style transfer in real-time without artifacts. Besides, we show that our trained model can naturally support multiple applications without fine-tuning, including low-light image enhancement, underwater image correction, image dehazing, and image harmonization. Project page with demos: https://zhkkke.github.io/NeuralPreset .

In this paper, we propose novel Gaussian process-gated hierarchical mixtures of experts (GPHMEs) that are used for building gates and experts. Unlike in other mixtures of experts where the gating models are linear to the input, the gating functions of our model are inner nodes built with Gaussian processes based on random features that are non-linear and non-parametric. Further, the experts are also built with Gaussian processes and provide predictions that depend on test data. The optimization of the GPHMEs is carried out by variational inference. There are several advantages of the proposed GPHMEs. One is that they outperform tree-based HME benchmarks that partition the data in the input space. Another advantage is that they achieve good performance with reduced complexity. A third advantage of the GPHMEs is that they provide interpretability of deep Gaussian processes and more generally of deep Bayesian neural networks. Our GPHMEs demonstrate excellent performance for large-scale data sets even with quite modest sizes.

We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian processes that are implemented via random feature-based Gaussian processes. With this model, we have two sets of unknowns, highly nonlinear unknowns (the values of the latent processes) and conditionally linear unknowns (the constant parameters of the random feature-based Gaussian processes). We present a method based on particle filtering where the constant parameters of the random feature-based Gaussian processes are integrated out in obtaining the predictive density of the states and do not need particles. We also propose an ensemble version of the method, with each member of the ensemble having its own set of features. With several experiments, we show that the method can track the latent processes up to a scale and rotation.