Polly's Polyhedral Scheduling in the Presence of Reductions

The polyhedral model provides a powerful mathematical abstraction to enable effective optimization of loop nests with respect to a given optimization goal, e.g., exploiting parallelism. Unexploited reduction properties are a frequent reason for polyhedral optimizers to assume parallelism prohibiting dependences. To our knowledge, no polyhedral loop optimizer available in any production compiler provides support for reductions. In this paper, we show that leveraging the parallelism of reductions can lead to a significant performance increase. We give a precise, dependence based, definition of reductions and discuss ways to extend polyhedral optimization to exploit the associativity and commutativity of reduction computations. We have implemented a reduction-enabled scheduling approach in the Polly polyhedral optimizer and evaluate it on the standard Polybench 3.2 benchmark suite. We were able to detect and model all 52 arithmetic reductions and achieve speedups up to 2.21$\times$ on a quad core machine by exploiting the multidimensional reduction in the BiCG benchmark.Comment: Presented at the IMPACT15 worksho

A morphospace of functional configuration to assess configural breadth based on brain functional networks

The best approach to quantify human brain functional reconfigurations in response to varying cognitive demands remains an unresolved topic in network neuroscience. We propose that such functional reconfigurations may be categorized into three different types: i) Network Configural Breadth, ii) Task-to-Task transitional reconfiguration, and iii) Within-Task reconfiguration. In order to quantify these reconfigurations, we propose a mesoscopic framework focused on functional networks (FNs) or communities. To do so, we introduce a 2D network morphospace that relies on two novel mesoscopic metrics, Trapping Efficiency (TE) and Exit Entropy (EE), which capture topology and integration of information within and between a reference set of FNs. In this study, we use this framework to quantify the Network Configural Breadth across different tasks. We show that the metrics defining this morphospace can differentiate FNs, cognitive tasks and subjects. We also show that network configural breadth significantly predicts behavioral measures, such as episodic memory, verbal episodic memory, fluid intelligence and general intelligence. In essence, we put forth a framework to explore the cognitive space in a comprehensive manner, for each individual separately, and at different levels of granularity. This tool that can also quantify the FN reconfigurations that result from the brain switching between mental states.Comment: main article: 24 pages, 8 figures, 2 tables. supporting information: 11 pages, 5 figure

Advancing Statistical Inference For Population Studies In Neuroimaging Using Machine Learning

Modern neuroimaging techniques allow us to investigate the brain in vivo and in high resolution, providing us with high dimensional information regarding the structure and the function of the brain in health and disease. Statistical analysis techniques transform this rich imaging information into accessible and interpretable knowledge that can be used for investigative as well as diagnostic and prognostic purposes. A prevalent area of research in neuroimaging is group comparison, i.e., the comparison of the imaging data of two groups (e.g. patients vs. healthy controls or people who respond to treatment vs. people who don\u27t) to identify discriminative imaging patterns that characterize different conditions. In recent years, the neuroimaging community has adopted techniques from mathematics, statistics, and machine learning to introduce novel methodologies targeting the improvement of our understanding of various neuropsychiatric and neurodegenerative disorders. However, existing statistical methods are limited by their reliance on ad-hoc assumptions regarding the homogeneity of disease effect, spatial properties of the underlying signal and the covariate structure of data, which imposes certain constraints about the sampling of datasets. 1. First, the overarching assumption behind most analytical tools, which are commonly used in neuroimaging studies, is that there is a single disease effect that differentiates the patients from controls. In reality, however, the disease effect may be heterogeneously expressed across the patient population. As a consequence, when searching for a single imaging pattern that characterizes the difference between healthy controls and patients, we may only get a partial or incomplete picture of the disease effect. 2. Second, and importantly, most analyses assume a uniform shape and size of disease effect. As a consequence, a common step in most neuroimaging analyses it to apply uniform smoothing of the data to aggregate regional information to each voxel to improve the signal to noise ratio. However, the shape and size of the disease patterns may not be uniformly represented across the brain. 3. Lastly, in practical scenarios, imaging datasets commonly include variations due to multiple covariates, which often have effects that overlap with the searched disease effects. To minimize the covariate effects, studies are carefully designed by appropriately matching the populations under observation. The difficulty of this task is further exacerbated by the advent of big data analyses that often entail the aggregation of large datasets collected across many clinical sites. The goal of this thesis is to address each of the aforementioned assumptions and limitations by introducing robust mathematical formulations, which are founded on multivariate machine learning techniques that integrate discriminative and generative approaches. Specifically, 1. First, we introduce an algorithm termed HYDRA which stands for heterogeneity through discriminative analysis. This method parses the heterogeneity in neuroimaging studies by simultaneously performing clustering and classification by use of piecewise linear decision boundaries. 2. Second, we propose to perform regionally linear multivariate discriminative statistical mapping (MIDAS) toward finding the optimal level of variable smoothing across the brain anatomy and tease out group differences in neuroimaging datasets. This method makes use of overlapping regional discriminative filters to approximate a matched filter that best delineates the underlying disease effect. 3. Lastly, we develop a method termed generative discriminative machines (GDM) toward reducing the effect of confounds in biased samples. The proposed method solves for a discriminative model that can also optimally generate the data when taking into account the covariate structure. We extensively validated the performance of the developed frameworks in the presence of diverse types of simulated scenarios. Furthermore, we applied our methods on a large number of clinical datasets that included structural and functional neuroimaging data as well as genetic data. Specifically, HYDRA was used for identifying distinct subtypes of Alzheimer\u27s Disease. MIDAS was applied for identifying the optimally discriminative patterns that differentiated between truth-telling and lying functional tasks. GDM was applied on a multi-site prediction setting with severely confounded samples. Our promising results demonstrate the potential of our methods to advance neuroimaging analysis beyond the set of assumptions that limit its capacity and improve statistical power

PageRank optimization applied to spam detection

We give a new link spam detection and PageRank demotion algorithm called MaxRank. Like TrustRank and AntiTrustRank, it starts with a seed of hand-picked trusted and spam pages. We define the MaxRank of a page as the frequency of visit of this page by a random surfer minimizing an average cost per time unit. On a given page, the random surfer selects a set of hyperlinks and clicks with uniform probability on any of these hyperlinks. The cost function penalizes spam pages and hyperlink removals. The goal is to determine a hyperlink deletion policy that minimizes this score. The MaxRank is interpreted as a modified PageRank vector, used to sort web pages instead of the usual PageRank vector. The bias vector of this ergodic control problem, which is unique up to an additive constant, is a measure of the "spamicity" of each page, used to detect spam pages. We give a scalable algorithm for MaxRank computation that allowed us to perform experimental results on the WEBSPAM-UK2007 dataset. We show that our algorithm outperforms both TrustRank and AntiTrustRank for spam and nonspam page detection.Comment: 8 pages, 6 figure

Methods for Structural Pattern Recognition: Complexity and Applications

Katedra kybernetik

A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems

International audienceSzeliski et al. published an influential study in 2006 on energy minimization methods for Markov Random Fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically , the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different car-dinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2,453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types

Statistical Machine Learning Methods for the Large Scale Analysis of Neural Data

Modern neurotechnologies enable the recording of neural activity at the scale of entire brains and with single-cell resolution. However, the lack of principled approaches to extract structure from these massive data streams prevent us from fully exploiting the potential of these technologies. This thesis, divided in three parts, introduces new statistical machine learning methods to enable the large-scale analysis of some of these complex neural datasets. In the first part, I present a method that leverages Gaussian quadrature to accelerate inference of neural encoding models from a certain type of observed neural point processes --- spike trains --- resulting in substantial improvements over existing methods. The second part focuses on the simultaneous electrical stimulation and recording of neurons using large electrode arrays. There, identification of neural activity is hindered by stimulation artifacts that are much larger than spikes, and overlap temporally with spikes. To surmount this challenge, I develop an algorithm to infer and cancel this artifact, enabling inference of the neural signal of interest. This algorithm is based on a a bayesian generative model for recordings, where a structured gaussian process is used to represent prior knowledge of the artifact. The algorithm achieves near perfect accuracy and enables the analysis of data hundreds of time faster than previous approaches. The third part is motivated by the problem of inference of neural dynamics in the worm C.elegans: when taking a data-driven approach to this question, e.g., when using whole-brain calcium imaging data, one is faced with the need to match neural recordings to canonical neural identities, in practice resolved by tedious human labor. Alternatively, on a bayesian setup this problem may be cast as posterior inference of a latent permutation. I introduce methods that enable gradient-based approximate posterior inference of permutations, overcoming the difficulties imposed by the combinatorial and discrete nature of this object. Results suggest the feasibility of automating neural identification, and demonstrate variational inference in permutations is a sensible alternative to MCMC