27 research outputs found
Moment-Based Variational Inference for Markov Jump Processes
We propose moment-based variational inference as a flexible framework for
approximate smoothing of latent Markov jump processes. The main ingredient of
our approach is to partition the set of all transitions of the latent process
into classes. This allows to express the Kullback-Leibler divergence between
the approximate and the exact posterior process in terms of a set of moment
functions that arise naturally from the chosen partition. To illustrate
possible choices of the partition, we consider special classes of jump
processes that frequently occur in applications. We then extend the results to
parameter inference and demonstrate the method on several examples.Comment: Accepted by the 36th International Conference on Machine Learning
(ICML 2019
Learning Sparse Graphon Mean Field Games
Although the field of multi-agent reinforcement learning (MARL) has made
considerable progress in the last years, solving systems with a large number of
agents remains a hard challenge. Graphon mean field games (GMFGs) enable the
scalable analysis of MARL problems that are otherwise intractable. By the
mathematical structure of graphons, this approach is limited to dense graphs
which are insufficient to describe many real-world networks such as power law
graphs. Our paper introduces a novel formulation of GMFGs, called LPGMFGs,
which leverages the graph theoretical concept of graphons and provides a
machine learning tool to efficiently and accurately approximate solutions for
sparse network problems. This especially includes power law networks which are
empirically observed in various application areas and cannot be captured by
standard graphons. We derive theoretical existence and convergence guarantees
and give empirical examples that demonstrate the accuracy of our learning
approach for systems with many agents. Furthermore, we extend the Online Mirror
Descent (OMD) learning algorithm to our setup to accelerate learning speed,
empirically show its capabilities, and conduct a theoretical analysis using the
novel concept of smoothed step graphons. In general, we provide a scalable,
mathematically well-founded machine learning approach to a large class of
otherwise intractable problems of great relevance in numerous research fields.Comment: accepted for publication at the International Conference on
Artificial Intelligence and Statistics (AISTATS) 2023; code available at:
https://github.com/ChrFabian/Learning_sparse_GMFG
Multi-StyleGAN: Towards Image-Based Simulation of Time-Lapse Live-Cell Microscopy
Time-lapse fluorescent microscopy (TLFM) combined with predictive
mathematical modelling is a powerful tool to study the inherently dynamic
processes of life on the single-cell level. Such experiments are costly,
complex and labour intensive. A complimentary approach and a step towards in
silico experimentation, is to synthesise the imagery itself. Here, we propose
Multi-StyleGAN as a descriptive approach to simulate time-lapse fluorescence
microscopy imagery of living cells, based on a past experiment. This novel
generative adversarial network synthesises a multi-domain sequence of
consecutive timesteps. We showcase Multi-StyleGAN on imagery of multiple live
yeast cells in microstructured environments and train on a dataset recorded in
our laboratory. The simulation captures underlying biophysical factors and time
dependencies, such as cell morphology, growth, physical interactions, as well
as the intensity of a fluorescent reporter protein. An immediate application is
to generate additional training and validation data for feature extraction
algorithms or to aid and expedite development of advanced experimental
techniques such as online monitoring or control of cells.
Code and dataset is available at
https://git.rwth-aachen.de/bcs/projects/tp/multi-stylegan.Comment: revised -- accepted to MICCAI 2021. (Tim Prangemeier and Christoph
Reich --- both authors contributed equally
Moment-Based Variational Inference for Stochastic Differential Equations
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and approximate the posterior by a set of moment functions. In combination with moment closure, the smoothing problem is reduced to a deterministic optimal control problem. Exploiting the path-wise Fisher information, we propose an optimization procedure that corresponds to a natural gradient descent in the variational parameters. Our approach allows for richer variational approximations that extend to state-dependent diffusion terms. The classical Gaussian process approximation is recovered as a special case
Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach
Learning the behavior of large agent populations is an important task for
numerous research areas. Although the field of multi-agent reinforcement
learning (MARL) has made significant progress towards solving these systems,
solutions for many agents often remain computationally infeasible and lack
theoretical guarantees. Mean Field Games (MFGs) address both of these issues
and can be extended to Graphon MFGs (GMFGs) to include network structures
between agents. Despite their merits, the real world applicability of GMFGs is
limited by the fact that graphons only capture dense graphs. Since most
empirically observed networks show some degree of sparsity, such as power law
graphs, the GMFG framework is insufficient for capturing these network
topologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) which
builds on the graph theoretical concept of graphexes. Graphexes are the
limiting objects to sparse graph sequences that also have other desirable
features such as the small world property. Learning equilibria in these games
is challenging due to the rich and sparse structure of the underlying graphs.
To tackle these challenges, we design a new learning algorithm tailored to the
GXMFG setup. This hybrid graphex learning approach leverages that the system
mainly consists of a highly connected core and a sparse periphery. After
defining the system and providing a theoretical analysis, we state our learning
approach and demonstrate its learning capabilities on both synthetic graphs and
real-world networks. This comparison shows that our GXMFG learning algorithm
successfully extends MFGs to a highly relevant class of hard, realistic
learning problems that are not accurately addressed by current MARL and MFG
methods.Comment: accepted at ICLR 202
Learning Decentralized Partially Observable Mean Field Control for Artificial Collective Behavior
Recent reinforcement learning (RL) methods have achieved success in various
domains. However, multi-agent RL (MARL) remains a challenge in terms of
decentralization, partial observability and scalability to many agents.
Meanwhile, collective behavior requires resolution of the aforementioned
challenges, and remains of importance to many state-of-the-art applications
such as active matter physics, self-organizing systems, opinion dynamics, and
biological or robotic swarms. Here, MARL via mean field control (MFC) offers a
potential solution to scalability, but fails to consider decentralized and
partially observable systems. In this paper, we enable decentralized behavior
of agents under partial information by proposing novel models for decentralized
partially observable MFC (Dec-POMFC), a broad class of problems with
permutation-invariant agents allowing for reduction to tractable single-agent
Markov decision processes (MDP) with single-agent RL solution. We provide
rigorous theoretical results, including a dynamic programming principle,
together with optimality guarantees for Dec-POMFC solutions applied to finite
swarms of interest. Algorithmically, we propose Dec-POMFC-based policy gradient
methods for MARL via centralized training and decentralized execution, together
with policy gradient approximation guarantees. In addition, we improve upon
state-of-the-art histogram-based MFC by kernel methods, which is of separate
interest also for fully observable MFC. We evaluate numerically on
representative collective behavior tasks such as adapted Kuramoto and Vicsek
swarming models, being on par with state-of-the-art MARL. Overall, our
framework takes a step towards RL-based engineering of artificial collective
behavior via MFC.Comment: Accepted to ICLR 202
Context-Aware Technology Mapping in Genetic Design Automation
Genetic design automation (GDA) tools hold promise to
speed-up
circuit design in synthetic biology. Their widespread adoption is
hampered by their limited predictive power, resulting in frequent
deviations between the in silico and in vivo performance of a genetic
circuit. Context effects, i.e., the change in overall circuit functioning,
due to the intracellular environment of the host and due to cross-talk
among circuits components are believed to be a major source for the
aforementioned deviations. Incorporating these effects in computational
models of GDA tools is challenging but is expected to boost their
predictive power and hence their deployment. Using fine-grained thermodynamic
models of promoter activity, we show in this work how to account for
two major components of cellular context effects: (i) crosstalk due
to limited specificity of used regulators and (ii) titration of circuit
regulators to off-target binding sites on the host genome. We show
how we can compensate the incurred increase in computational complexity
through dedicated branch-and-bound techniques during the technology
mapping process. Using the synthesis of several combinational logic
circuits based on Cello’s device library as a case study, we
analyze the effect of different intensities and distributions of crosstalk
on circuit performance and on the usability of a given device library
Multiclass Yeast Segmentation in Microstructured Environments with Deep Learning
Cell segmentation is a major bottleneck in extracting quantitative
single-cell information from microscopy data. The challenge is exasperated in
the setting of microstructured environments. While deep learning approaches
have proven useful for general cell segmentation tasks, existing segmentation
tools for the yeast-microstructure setting rely on traditional machine learning
approaches. Here we present convolutional neural networks trained for
multiclass segmenting of individual yeast cells and discerning these from
cell-similar microstructures. We give an overview of the datasets recorded for
training, validating and testing the networks, as well as a typical use-case.
We showcase the method's contribution to segmenting yeast in microstructured
environments with a typical synthetic biology application in mind. The models
achieve robust segmentation results, outperforming the previous
state-of-the-art in both accuracy and speed. The combination of fast and
accurate segmentation is not only beneficial for a posteriori data processing,
it also makes online monitoring of thousands of trapped cells or closed-loop
optimal experimental design feasible from an image processing perspective.Comment: IEEE CIBCB 2020 (accepted
Multiclass Yeast Segmentation in Microstructured Environments with Deep Learning
Cell segmentation is a major bottleneck in extracting quantitative single-cell information from microscopy data. The challenge is exasperated in the setting of microstructured environments. While deep learning approaches have proven useful for general cell segmentation tasks, existing segmentation tools for the yeast-microstructure setting rely on traditional machine learning approaches. Here we present convolutional neural networks trained for multiclass segmenting of individual yeast cells and discerning these from cell-similar microstructures. We give an overview of the datasets recorded for training, validating and testing the networks, as well as a typical use-case. We showcase the method's contribution to segmenting yeast in microstructured environments with a typical synthetic biology application in mind. The models achieve robust segmentation results, outperforming the previous state-of-the-art in both accuracy and speed. The combination of fast and accurate segmentation is not only beneficial for a posteriori data processing, it also makes online monitoring of thousands of trapped cells or closed-loop optimal experimental design feasible from an image processing perspective