The Complexity of the Simplex Method

The simplex method is a well-studied and widely-used pivoting method for solving linear programs. When Dantzig originally formulated the simplex method, he gave a natural pivot rule that pivots into the basis a variable with the most violated reduced cost. In their seminal work, Klee and Minty showed that this pivot rule takes exponential time in the worst case. We prove two main results on the simplex method. Firstly, we show that it is PSPACE-complete to find the solution that is computed by the simplex method using Dantzig's pivot rule. Secondly, we prove that deciding whether Dantzig's rule ever chooses a specific variable to enter the basis is PSPACE-complete. We use the known connection between Markov decision processes (MDPs) and linear programming, and an equivalence between Dantzig's pivot rule and a natural variant of policy iteration for average-reward MDPs. We construct MDPs and show PSPACE-completeness results for single-switch policy iteration, which in turn imply our main results for the simplex method

A Kernel Method for the Two-sample Problem

We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a third is based on the asymptotic distribution of this statistic. The test statistic can be computed in quadratic time, although efficient linear time approximations are available. Several classical metrics on distributions are recovered when the function space used to compute the difference in expectations is allowed to be more general (eg.~a Banach space). We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests

Hilbert Space Representations of Probability Distributions

Many problems in unsupervised learning require the analysis of features of probability distributions. At the most fundamental level, we might wish to determine whether two distributions are the same, based on samples from each - this is known as the two-sample or homogeneity problem. We use kernel methods to address this problem, by mapping probability distributions to elements in a reproducing kernel Hilbert space (RKHS). Given a sufficiently rich RKHS, these representations are unique: thus comparing feature space representations allows us to compare distributions without ambiguity. Applications include testing whether cancer subtypes are distinguishable on the basis of DNA microarray data, and whether low frequency oscillations measured at an electrode in the cortex have a different distribution during a neural spike. A more difficult problem is to discover whether two random variables drawn from a joint distribution are independent. It turns out that any dependence between pairs of random variables can be encoded in a cross-covariance operator between appropriate RKHS representations of the variables, and we may test independence by looking at a norm of the operator. We demonstrate this independence test by establishing dependence between an English text and its French translation, as opposed to French text on the same topic but otherwise unrelated. Finally, we show that this operator norm is itself a difference in feature means

RNA atlas of human bacterial pathogens uncovers stress dynamics linked to infection

Bacterial processes necessary for adaption to stressful host environments are potential targets for new antimicrobials. Here, we report large-scale transcriptomic analyses of 32 human bacterial pathogens grown under 11 stress conditions mimicking human host environments. The potential relevance of the in vitro stress conditions and responses is supported by comparisons with available in vivo transcriptomes of clinically important pathogens. Calculation of a probability score enables comparative cross-microbial analyses of the stress responses, revealing common and unique regulatory responses to different stresses, as well as overlapping processes participating in different stress responses. We identify conserved and species-specific 'universal stress responders', that is, genes showing altered expression in multiple stress conditions. Non-coding RNAs are involved in a substantial proportion of the responses. The data are collected in a freely available, interactive online resource (PATHOgenex). Bacterial stress responses are potential targets for new antimicrobials. Here, Avican et al. present global transcriptomes for 32 bacterial pathogens grown under 11 stress conditions, and identify common and unique regulatory responses, as well as processes participating in different stress responses.Peer reviewe

Prediction of recovery from multiple organ dysfunction syndrome in pediatric sepsis patients.

MOTIVATION Sepsis is a leading cause of death and disability in children globally, accounting for ∼3 million childhood deaths per year. In pediatric sepsis patients, the multiple organ dysfunction syndrome (MODS) is considered a significant risk factor for adverse clinical outcomes characterized by high mortality and morbidity in the pediatric intensive care unit. The recent rapidly growing availability of electronic health records (EHRs) has allowed researchers to vastly develop data-driven approaches like machine learning in healthcare and achieved great successes. However, effective machine learning models which could make the accurate early prediction of the recovery in pediatric sepsis patients from MODS to a mild state and thus assist the clinicians in the decision-making process is still lacking. RESULTS This study develops a machine learning-based approach to predict the recovery from MODS to zero or single organ dysfunction by 1 week in advance in the Swiss Pediatric Sepsis Study cohort of children with blood-culture confirmed bacteremia. Our model achieves internal validation performance on the SPSS cohort with an area under the receiver operating characteristic (AUROC) of 79.1% and area under the precision-recall curve (AUPRC) of 73.6%, and it was also externally validated on another pediatric sepsis patients cohort collected in the USA, yielding an AUROC of 76.4% and AUPRC of 72.4%. These results indicate that our model has the potential to be included into the EHRs system and contribute to patient assessment and triage in pediatric sepsis patient care. AVAILABILITY AND IMPLEMENTATION Code available at https://github.com/BorgwardtLab/MODS-recovery. The data underlying this article is not publicly available for the privacy of individuals that participated in the study. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online

A Principled Approach to Analyze Expressiveness and Accuracy of Graph Neural Networks

Graph neural networks (GNNs) have known an increasing success recently, with many GNN variants achieving state-of-the-art results on node and graph classification tasks. The proposed GNNs, however, often implement complex node and graph embedding schemes, which makes challenging to explain their performance. In this paper, we investigate the link between a GNN's expressiveness, that is, its ability to map different graphs to different representations, and its generalization performance in a graph classification setting. In particular , we propose a principled experimental procedure where we (i) define a practical measure for expressiveness, (ii) introduce an expressiveness-based loss function that we use to train a simple yet practical GNN that is permutation-invariant, (iii) illustrate our procedure on benchmark graph classification problems and on an original real-world application. Our results reveal that expressiveness alone does not guarantee a better performance, and that a powerful GNN should be able to produce graph representations that are well separated with respect to the class of the corresponding graphs

Adolescent self-control predicts midlife hallucinatory experiences:40-year follow-up of a national birth cohort

Associations between self-control in adolescence and adult mental health are unclear in the general population; to our knowledge, no study has investigated self-control in relation to psychotic-like symptoms

Prediction of recovery from multiple organ dysfunction syndrome in pediatric sepsis patients

MOTIVATION: Sepsis is a leading cause of death and disability in children globally, accounting for ∼3 million childhood deaths per year. In pediatric sepsis patients, the multiple organ dysfunction syndrome (MODS) is considered a significant risk factor for adverse clinical outcomes characterized by high mortality and morbidity in the pediatric intensive care unit. The recent rapidly growing availability of electronic health records (EHRs) has allowed researchers to vastly develop data-driven approaches like machine learning in healthcare and achieved great successes. However, effective machine learning models which could make the accurate early prediction of the recovery in pediatric sepsis patients from MODS to a mild state and thus assist the clinicians in the decision-making process is still lacking. RESULTS: This study develops a machine learning-based approach to predict the recovery from MODS to zero or single organ dysfunction by 1 week in advance in the Swiss Pediatric Sepsis Study cohort of children with blood-culture confirmed bacteremia. Our model achieves internal validation performance on the SPSS cohort with an area under the receiver operating characteristic (AUROC) of 79.1% and area under the precision-recall curve (AUPRC) of 73.6%, and it was also externally validated on another pediatric sepsis patients cohort collected in the USA, yielding an AUROC of 76.4% and AUPRC of 72.4%. These results indicate that our model has the potential to be included into the EHRs system and contribute to patient assessment and triage in pediatric sepsis patient care. AVAILABILITY AND IMPLEMENTATION: Code available at https://github.com/BorgwardtLab/MODS-recovery. The data underlying this article is not publicly available for the privacy of individuals that participated in the study. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online

Cannabis affects people differently: inter-subject variation in the psychotogenic effects of Δ9-tetrahydrocannabinol: a functional magnetic resonance imaging study with healthy volunteers

Background Cannabis can induce transient psychotic symptoms, but not all users experience these adverse effects. We compared the neural response to Δ9-tetrahydrocannabinol (THC) in healthy volunteers in whom the drug did or did not induce acute psychotic symptoms. Method In a double-blind, placebo-controlled, pseudorandomized design, 21 healthy men with minimal experience of cannabis were given either 10mg THC or placebo, orally. Behavioural and functional magnetic resonance imaging measures were then recorded whilst they performed a go/no-go task. Results The sample was subdivided on the basis of the Positive and Negative Syndrome Scale positive score following administration of THC into transiently psychotic (TP; n=11) and non-psychotic (NP; n=10) groups. During the THC condition, TP subjects made more frequent inhibition errors than the NP group and showed differential activation relative to the NP group in the left parahippocampal gyrus, the left and right middle temporal gyri and in the right cerebellum. In these regions, THC had opposite effects on activation relative to placebo in the two groups. The TP group also showed less activation than the NP group in the right middle temporal gyrus and cerebellum, independent of the effects of THC. Conclusions In this first demonstration of inter-subject variability in sensitivity to the psychotogenic effects of THC, we found that the presence of acute psychotic symptoms was associated with a differential effect of THC on activation in the ventral and medial temporal cortex and cerebellum, suggesting that these regions mediate the effects of the drug on psychotic symptom