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Marin Bilos

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4 papers

1 author row

ICML Conference 2024 Conference Paper

Variational Schrödinger Diffusion Models

Wei Deng 0002
Weijian Luo
Yixin Tan
Marin Bilos
Yu Chen
Yuriy Nevmyvaka
Ricky T. Q. Chen

Schrödinger bridge (SB) has emerged as the go-to method for optimizing transportation plans in diffusion models. However, SB requires estimating the intractable forward score functions, inevitably resulting in the (costly) implicit training loss based on simulated trajectories. To improve the scalability while preserving efficient transportation plans, we leverage variational inference to linearize the forward score functions (variational scores) of SB and restore simulation-free properties in training backward scores. We propose the variational Schrödinger diffusion model (VSDM), where the forward process is a multivariate diffusion and the variational scores are adaptively optimized for efficient transport. Theoretically, we use stochastic approximation to prove the convergence of the variational scores and show the convergence of the adaptively generated samples based on the optimal variational scores. Empirically, we test the algorithm in simulated examples and observe that VSDM is efficient in generations of anisotropic shapes and yields straighter sample trajectories compared to the single-variate diffusion. We also verify the scalability of the algorithm in real-world data and achieve competitive unconditional generation performance in CIFAR10 and conditional generation in time series modeling. Notably, VSDM no longer depends on warm-up initializations required by SB.

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ICML Conference 2023 Conference Paper

Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion

Marin Bilos
Kashif Rasul
Anderson Schneider
Yuriy Nevmyvaka
Stephan Günnemann

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

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ICML Conference 2021 Conference Paper

Scalable Normalizing Flows for Permutation Invariant Densities

Marin Bilos
Stephan Günnemann

Modeling sets is an important problem in machine learning since this type of data can be found in many domains. A promising approach defines a family of permutation invariant densities with continuous normalizing flows. This allows us to maximize the likelihood directly and sample new realizations with ease. In this work, we demonstrate how calculating the trace, a crucial step in this method, raises issues that occur both during training and inference, limiting its practicality. We propose an alternative way of defining permutation equivariant transformations that give closed form trace. This leads not only to improvements while training, but also to better final performance. We demonstrate the benefits of our approach on point processes and general set modeling.

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ICLR Conference 2020 Conference Paper

Intensity-Free Learning of Temporal Point Processes

Oleksandr Shchur
Marin Bilos
Stephan Günnemann

Temporal point processes are the dominant paradigm for modeling sequences of events happening at irregular intervals. The standard way of learning in such models is by estimating the conditional intensity function. However, parameterizing the intensity function usually incurs several trade-offs. We show how to overcome the limitations of intensity-based approaches by directly modeling the conditional distribution of inter-event times. We draw on the literature on normalizing flows to design models that are flexible and efficient. We additionally propose a simple mixture model that matches the flexibility of flow-based models, but also permits sampling and computing moments in closed form. The proposed models achieve state-of-the-art performance in standard prediction tasks and are suitable for novel applications, such as learning sequence embeddings and imputing missing data.

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