Generalized Identifiability Bounds for Mixture Models with Grouped Samples

Recent work has shown that finite mixture models with $m$ components are identifiable, while making no assumptions on the mixture components, so long as one has access to groups of samples of size $2m-1$ which are known to come from the same mixture component. In this work we generalize that result and show that, if every subset of $k$ mixture components of a mixture model are linearly independent, then that mixture model is identifiable with only $(2m-1)/(k-1)$ samples per group. We further show that this value cannot be improved. We prove an analogous result for a stronger form of identifiability known as "determinedness" along with a corresponding lower bound. This independence assumption almost surely holds if mixture components are chosen randomly from a $k$-dimensional space. We describe some implications of our results for multinomial mixture models and topic modeling

Analysing cerebrospinal fluid with explainable deep learning: From diagnostics to insights

Aim Analysis of cerebrospinal fluid (CSF) is essential for diagnostic workup of patients with neurological diseases and includes differential cell typing. The current gold standard is based on microscopic examination by specialised technicians and neuropathologists, which is time-consuming, labour-intensive and subjective. Methods We, therefore, developed an image analysis approach based on expert annotations of 123,181 digitised CSF objects from 78 patients corresponding to 15 clinically relevant categories and trained a multiclass convolutional neural network (CNN). Results The CNN classified the 15 categories with high accuracy (mean AUC 97.3%). By using explainable artificial intelligence (XAI), we demonstrate that the CNN identified meaningful cellular substructures in CSF cells recapitulating human pattern recognition. Based on the evaluation of 511 cells selected from 12 different CSF samples, we validated the CNN by comparing it with seven board-certified neuropathologists blinded for clinical information. Inter-rater agreement between the CNN and the ground truth was non-inferior (Krippendorff's alpha 0.79) compared with the agreement of seven human raters and the ground truth (mean Krippendorff's alpha 0.72, range 0.56–0.81). The CNN assigned the correct diagnostic label (inflammatory, haemorrhagic or neoplastic) in 10 out of 11 clinical samples, compared with 7–11 out of 11 by human raters. Conclusions Our approach provides the basis to overcome current limitations in automated cell classification for routine diagnostics and demonstrates how a visual explanation framework can connect machine decision-making with cell properties and thus provide a novel versatile and quantitative method for investigating CSF manifestations of various neurological diseases.Peer Reviewe

Improved models for operation modes of complex compressor stations

We study combinatorial structures in large-scale mixed-integer (nonlinear) programming problems arising in gas network optimization. We propose a preprocessing strategy exploiting the observation that a large part of the combinatorial complexity arises in certain subnetworks. Our approach analyzes these subnetworks and the combinatorial structure of the flows within these subnetworks in order to provide alternative models with a stronger combinatorial structure that can be exploited by off-the-shelve solvers. In particular, we consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. We propose a refined model that allows to precompute tighter bounds for each operation mode and a number of model variants based on the refined model exploiting these tighter bounds. We provide a procedure to obtain the refined model from the input data for the original model. This procedure is based on a nontrivial reduction of the graph representing the gas flow through the compressor station in an operation mode. We evaluate our model variants on reference benchmark data, showing that they reduce the average running time between 10% for easy instances and 46% for hard instances. Moreover, for three of four considered networks, the average number of search tree nodes is at least halved, showing the effectivity of our model variants to guide the solver’s search