Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation offers a promising and less expensive alternative, but requires an assessment of the simulation accuracy and therefore end-to-end measurements. Additionally, covariate shifts between simulations and actual usage can cause difficulties for estimating the reliability of such systems. In this work, we present a validation method that propagates bounds on distributional discrepancy measures through a composite system, thereby allowing us to derive an upper bound on the failure probability of the real system from potentially inaccurate simulations. Each propagation step entails an optimization problem, where – for measures such as maximum mean discrepancy (MMD) – we develop tight convex relaxations based on semidefinite programs. We demonstrate that our propagation method yields valid and useful bounds for composite systems exhibiting a variety of realistic effects. In particular, we show that the proposed method can successfully account for data shifts within the experimental design as well as model inaccuracies within the simulation.

Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but just a lack of functionality in classic ODE solvers, which do not return a likelihood but a point estimate. To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood. This approximation yields tractable estimators for the gradient and Hessian of the (log-)likelihood. Insertion of these estimators into existing gradient-based optimization and sampling methods engenders new solvers for ODE inverse problems. We demonstrate that these methods outperform standard likelihood-free approaches on three benchmark-systems.

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g., LSTMs) proved extremely successful in modeling complex time series data. Fully probabilistic SSMs, however, are often found hard to train, even for smaller problems. We propose a novel model formulation and a scalable training algorithm based on doubly stochastic variational inference and Gaussian processes. This combination allows efficient incorporation of latent state temporal correlations, which we found to be key to robust training. The effectiveness of the proposed PR-SSM is evaluated on a set of real-world benchmark datasets in comparison to state-of-the-art probabilistic model learning methods. Scalability and robustness are demonstrated on a high dimensional problem.

MOTIVATION: To gain fundamental insight into the development of embryos, biologists seek to understand the fate of each and every embryonic cell. For the generation of cell tracks in embryogenesis, so-called tracking-by-assignment methods are flexible approaches. However, as every two-stage approach, they suffer from irrevocable errors propagated from the first stage to the second stage, here from segmentation to tracking. It is therefore desirable to model segmentation and tracking in a joint holistic assignment framework allowing the two stages to maximally benefit from each other. RESULTS: We propose a probabilistic graphical model, which both automatically selects the best segments from a time series of oversegmented images/volumes and links them across time. This is realized by introducing intra-frame and inter-frame constraints between conflicting segmentation and tracking hypotheses while at the same time allowing for cell division. We show the efficiency of our algorithm on a challenging 3D+t cell tracking dataset from Drosophila embryogenesis and on a 2D+t dataset of proliferating cells in a dense population with frequent overlaps. On the latter, we achieve results significantly better than state-of-the-art tracking methods. AVAILABILITY AND IMPLEMENTATION: Source code and the 3D+t Drosophila dataset along with our manual annotations will be freely available on http://hci.iwr.uni-heidelberg.de/MIP/Research/tracking/

We use weakly supervised structured learning to track and disambiguate the identity of multiple indistinguishable, translucent and deformable objects that can overlap for many frames. For this challenging problem, we propose a novel model which handles occlusions, complex motions and non-rigid deformations by jointly optimizing the flows of multiple latent intensities across frames. These flows are latent variables for which the user cannot directly provide labels. Instead, we leverage a structured learning formulation that uses weak user annotations to find the best hyperparameters of this model. The approach is evaluated on a challenging dataset for the tracking of multiple Drosophila larvae which we make publicly available. Our method tracks multiple larvae in spite of their poor distinguishability and minimizes the number of identity switches during prolonged mutual occlusion.

One distinguishing property of life is its temporal dynamics, and it is hence only natural that time lapse experiments play a crucial role in modern biomedical research areas such as signaling pathways, drug discovery or developmental biology. Such experiments yield a very large number of images that encode complex cellular activities, and reliable automated cell tracking emerges naturally as a prerequisite for further quantitative analysis. However, many existing cell tracking methods are restricted to using only a small number of features to allow for manual tweaking. In this paper, we propose a novel cell tracking approach that embraces a powerful machine learning technique to optimize the tracking parameters based on user annotated tracks. Our approach replaces the tedious parameter tuning with parameter learning and allows for the use of a much richer set of complex tracking features, which in turn affords superior prediction accuracy. Furthermore, we developed an active learning approach for efficient training data retrieval, which reduces the annotation effort to only 17%. In practical terms, our approach allows life science researchers to inject their expertise in a more intuitive and direct manner. This process is further facilitated by using a glyph visualization technique for ground truth annotation and validation. Evaluation and comparison on several publicly available benchmark sequences show significant performance improvement over recently reported approaches. Code and software tools are provided to the public.

The quality of any tracking-by-assignment hinges on the accuracy of the foregoing target detection / segmentation step. In many kinds of images, errors in this first stage are unavoidable. These errors then propagate to, and corrupt, the tracking result. Our main contribution is the first probabilistic graphical model that can explicitly account for over- and under segmentation errors even when the number of tracking targets is unknown and when they may divide, as in cell cultures. The tracking model we present implements global consistency constraints for the number of targets comprised by each detection and is solved to global optimality on reasonably large 2D+t and 3D+t datasets. In addition, we empirically demonstrate the effectiveness of a post processing that allows to establish target identity even across occlusion / under segmentation. The usefulness and efficiency of this new tracking method is demonstrated on three different and challenging 2D+t and 3D+t datasets from developmental biology.