Bandit Online Optimization Over the Permutahedron

The permutahedron is the convex polytope with vertex set consisting of the vectors $(\pi(1),\dots, \pi(n))$ for all permutations (bijections) $\pi$ over $\{1,\dots, n\}$. We study a bandit game in which, at each step $t$, an adversary chooses a hidden weight weight vector $s_t$, a player chooses a vertex $\pi_t$ of the permutahedron and suffers an observed loss of $\sum_{i=1}^n \pi(i) s_t(i)$. A previous algorithm CombBand of Cesa-Bianchi et al (2009) guarantees a regret of $O(n\sqrt{T \log n})$ for a time horizon of $T$. Unfortunately, CombBand requires at each step an $n$-by-$n$ matrix permanent approximation to within improved accuracy as $T$ grows, resulting in a total running time that is super linear in $T$, making it impractical for large time horizons. We provide an algorithm of regret $O(n^{3/2}\sqrt{T})$ with total time complexity $O(n^3T)$. The ideas are a combination of CombBand and a recent algorithm by Ailon (2013) for online optimization over the permutahedron in the full information setting. The technical core is a bound on the variance of the Plackett-Luce noisy sorting process's "pseudo loss". The bound is obtained by establishing positive semi-definiteness of a family of 3-by-3 matrices generated from rational functions of exponentials of 3 parameters

Coordinate based meta-analysis of networks in neuroimaging studies

Meta-analysis of summary results from published neuroimaging studies independently testing a common hypothesis is performed using coordinate based meta-analysis (CBMA), which tests for consistent activation (in the case of functional MRI studies) of the same anatomical regions. Using just the reported coordinates it is also possible to meta-analyse coactivated regions to reveal a network-like structure of coordinate clusters (network nodes) distributed at the coactivated locations and a measure of the coactivation strength (network edges), which is determined by the presence/absence of reported activation.Here a new coordinate-based method to estimate a network of coactivations is detailed, which utilises the Z score accompanying each reported. Coordinate based meta-analysis of networks (CBMAN) assumes that if the activation pattern reported by independent studies is truly consistent, then the relative magnitude of these Z scores might also be consistent. It is hypothesised that this is detectable as Z score covariance between coactivated regions provided the within study variances are small. Advantages of using the Z scores instead of coordinates to measure coactivation strength are that censoring by the significance thresholds can be considered, and that using a continuous measure rather than a dichotomous one can increase statistical power.CBMAN uses maximum likelihood estimation to fit multivariate normal distributions to the standardised Z scores, and the covariances are considered as edges of a network of coactivated clusters (nodes). Here it is validated by numerical simulation and demonstrated on real data used previously to demonstrate CBMA. Software to perform CBMAN is freely available

Easy to interpret Coordinate Based Meta-Analysis of neuroimaging studies: Analysis of Brain Coordinates (ABC)

Background: Functional MRI and voxel-based morphometry are important in neuroscience. They are technically challenging with no globally optimal analysis method, and the multiple approaches have been shown to produce different results. It is useful to be able to meta-analyse results from such studies that tested a similar hypothesis potentially using different analysis methods. The aim is to identify replicable results and infer hypothesis specific effects. Coordinate based meta-analysis (CBMA) offers this, but the multiple algorithms can produce different results, making interpretation conditional on the algorithm. New method: Here a new model based CBMA algorithm, Analysis of Brain Coordinates (ABC), is presented. ABC aims to be simple to understand by avoiding empirical elements where possible and by using a simple to interpret statistical threshold, which relates to the primary aim of detecting replicable effects.Results: ABC is compared to both the most used and the most recently developed CBMA algorithms, by reproducing a published meta-analysis of localised grey matter changes in schizophrenia. There are some differences in results and the type of data that can be analysed, which are related to the algorithm specifics.Comparison to other methods: Compared to other algorithms ABC eliminates empirical elements where possible and uses a simple to interpret statistical threshold. Conclusions: There may be no optimal way to meta-analyse neuroimaging studies using CBMA. However, by eliminating some empirical elements and relating the statistical threshold directly to the aim of finding replicable effects, ABC makes the impact of the algorithm on any conclusion easier to understand

Coordinate based meta-analysis of motor functional imaging in Parkinson's: disease-specific patterns and modulation by dopamine replacement and deep brain stimulation

ObjectiveTo investigate factors affecting the pattern of motor brain activation reported in people with Parkinson’s (PwP), aiming to differentiate disease-specific features from treatment effects.MethodsA co-ordinate-based-meta-analysis (CBMA) of functional motor neuroimaging studies involving patients with Parkinson’s (PwP), and healthy controls (HC) identified 126 suitable articles. The experiments were grouped based on subject feature, medication status (onMed/offMed), deep brain stimulation (DBS) status (DBSon/DBSoff) and type of motor initiation.ResultsHC and PwP shared similar neural networks during upper extremity motor tasks but with differences of reported frequency in mainly bilateral putamen, insula and ipsilateral inferior parietal and precentral gyri. The activation height was significantly reduced in the bilateral putamen, left SMA, left subthalamus nucleus, right thalamus and right midial global pallidum in PwPoffMed (vs. HC), and pre-SMA hypoactivation correlated with disease severity. These changes were not found in patients on dopamine replacement therapy (PwPonMed vs. HC) in line with a restorative function. By contrast, left SMA and primary motor cortex showed hyperactivation in the medicated state (vs. HC) suggesting dopaminergic overcompensation. Deep-brain stimulation (PwP during the high frequency subthalamus nucleus (STN) DBS vs. no stimulation) induced a decrease in left SMA activity and the expected increase in the left subthalamic/thalamic region regardless of hand movement. We further demonstrated a disease related effect of motor intention with only PwPoffMed showing increased activation in the medial frontal lobe in self-initiated studies.ConclusionWe describe a consistent disease-specific pattern of putaminal hypoactivation during motor tasks that appears reversed by dopamine replacement. Inconsistent reports of altered SMA/pre-SMA activation can be explained by task- and medication-specific variation in intention. Moreover, SMA activity was reduced during STN-DBS, while dopamine-induced hyperactivation of SMA which might underpin hyperdynamic L-dopa related overcompensation

Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006 proceeding

Thoracic Electrical Impedance Tomography—The 2022 Veterinary Consensus Statement

Electrical impedance tomography (EIT) is a non-invasive real-time non-ionising imaging modality that has many applications. Since the first recorded use in 1978, the technology has become more widely used especially in human adult and neonatal critical care monitoring. Recently, there has been an increase in research on thoracic EIT in veterinary medicine. Real-time imaging of the thorax allows evaluation of ventilation distribution in anesthetised and conscious animals. As the technology becomes recognised in the veterinary community there is a need to standardize approaches to data collection, analysis, interpretation and nomenclature, ensuring comparison and repeatability between researchers and studies. A group of nineteen veterinarians and two biomedical engineers experienced in veterinary EIT were consulted and contributed to the preparation of this statement. The aim of this consensus is to provide an introduction to this imaging modality, to highlight clinical relevance and to include recommendations on how to effectively use thoracic EIT in veterinary species. Based on this, the consensus statement aims to address the need for a streamlined approach to veterinary thoracic EIT and includes: an introduction to the use of EIT in veterinary species, the technical background to creation of the functional images, a consensus from all contributing authors on the practical application and use of the technology, descriptions and interpretation of current available variables including appropriate statistical analysis, nomenclature recommended for consistency and future developments in thoracic EIT. The information provided in this consensus statement may benefit researchers and clinicians working within the field of veterinary thoracic EIT. We endeavor to inform future users of the benefits of this imaging modality and provide opportunities to further explore applications of this technology with regards to perfusion imaging and pathology diagnosis

The development, educational stratification and decomposition of mothers' and fathers' childcare time in Germany: an update for 2001-2013

"This study updates empirical knowledge about the development,(the educational stratification, and the decomposition of mothers' and fathers' childcare time in Germany with the most recent time use data. Using time series data from the German Time Use Study 2001/2002 and 2012/ 2013, we analyze time budgets for total childcare and six specific childcare activities on weekdays and weekends and estimate OLS regressions and Oaxaca decompositions. The study found that total childcare time has increased for mothers and fathers between 2001 and 2013 and that this change is predominantly due to increased time for basic childcare. It also found consistent evidence of an education gradient only for reading time with children. If there is significant change of time budgets between 2001 and 2013, this change seems to be driven by behavioral change rather than changing demographics. Our empirical findings on childcare time in Germany do not provide evidence of dynamics and stratification but rather of stability and similarity across parents’ educational levels. Besides the updates on German parents' development, stratification and decomposition of time use for childcare, these analyses show that change in total childcare is not due to a proportional change over all single activities but due to changes in a few activities only." (author's abstract)"Diese Studie aktualisiert das empirische Wissen über die Entwicklung, die Bildungsstratifizierung und die Dekomposition der Zeitverwendung von Müttern und Vätern für Kinderbetreuung mit den aktuellen Zeitbudgetdaten für Deutschland. Auf Basis der der letzten beiden Erhebungen der Deutschen Zeitverwendungsstudie 2001/2002 und 2012/2013 werden die Zeitbudgets für die Gesamtzeit für Kinderbetreuung sowie sechs Einzeltätigkeiten mit OLS-Regressionen und Oaxaca- Dekompositionen untersucht. Die Studie zeigt, dass die Zeit für Kinderbetreuung von Müttern und Vätern zwischen 2001 und 2013 angestiegen ist, es einen Bildungsgradienten für Vorlesen gibt und signifikante Veränderungen in den Zeitbudgets nicht auf Kompositionsveränderung der Bevölkerung zurückgeführt werden können. Insgesamt belegt die Studie weniger die Dynamik als vielmehr die Stabilität und die geringe Bildungsdifferenzierung der Zeitverwendung für Kinderbetreuung. Darüber hinaus wird gezeigt, dass die Veränderungen in der Gesamtzeit für Kinderbetreuung nicht auf proportionale Veränderungen in allen, sondern nur auf Veränderungen in wenigen Einzeltätigkeiten zurückgeführt werden können." (Autorenreferat