Adaptive Threshold Sampling and Estimation

Sampling is a fundamental problem in both computer science and statistics. A number of issues arise when designing a method based on sampling. These include statistical considerations such as constructing a good sampling design and ensuring there are good, tractable estimators for the quantities of interest as well as computational considerations such as designing fast algorithms for streaming data and ensuring the sample fits within memory constraints. Unfortunately, existing sampling methods are only able to address all of these issues in limited scenarios. We develop a framework that can be used to address these issues in a broad range of scenarios. In particular, it addresses the problem of drawing and using samples under some memory budget constraint. This problem can be challenging since the memory budget forces samples to be drawn non-independently and consequently, makes computation of resulting estimators difficult. At the core of the framework is the notion of a data adaptive thresholding scheme where the threshold effectively allows one to treat the non-independent sample as if it were drawn independently. We provide sufficient conditions for a thresholding scheme to allow this and provide ways to build and compose such schemes. Furthermore, we provide fast algorithms to efficiently sample under these thresholding schemes

Explain3D: Explaining Disagreements in Disjoint Datasets

Data plays an important role in applications, analytic processes, and many aspects of human activity. As data grows in size and complexity, we are met with an imperative need for tools that promote understanding and explanations over data-related operations. Data management research on explanations has focused on the assumption that data resides in a single dataset, under one common schema. But the reality of today's data is that it is frequently un-integrated, coming from different sources with different schemas. When different datasets provide different answers to semantically similar questions, understanding the reasons for the discrepancies is challenging and cannot be handled by the existing single-dataset solutions. In this paper, we propose Explain3D, a framework for explaining the disagreements across disjoint datasets (3D). Explain3D focuses on identifying the reasons for the differences in the results of two semantically similar queries operating on two datasets with potentially different schemas. Our framework leverages the queries to perform a semantic mapping across the relevant parts of their provenance; discrepancies in this mapping point to causes of the queries' differences. Exploiting the queries gives Explain3D an edge over traditional schema matching and record linkage techniques, which are query-agnostic. Our work makes the following contributions: (1) We formalize the problem of deriving optimal explanations for the differences of the results of semantically similar queries over disjoint datasets. (2) We design a 3-stage framework for solving the optimal explanation problem. (3) We develop a smart-partitioning optimizer that improves the efficiency of the framework by orders of magnitude. (4)~We experiment with real-world and synthetic data to demonstrate that Explain3D can derive precise explanations efficiently

A framework for detection and classification of events in neural activity

We present a method for the real time prediction of punctate events in neural activity, based on the time-frequency spectrum of the signal, applicable both to continuous processes like local field potentials (LFP) as well as to spike trains. We test it on recordings of LFP and spiking activity acquired previously from the lateral intraparietal area (LIP) of macaque monkeys performing a memory-saccade task. In contrast to earlier work, where trials with known start times were classified, our method detects and classifies trials directly from the data. It provides a means to quantitatively compare and contrast the content of LFP signals and spike trains: we find that the detector performance based on the LFP matches the performance based on spike rates. The method should find application in the development of neural prosthetics based on the LFP signal. Our approach uses a new feature vector, which we call the 2D cepstrum.Comment: 30 pages, 6 figures; This version submitted to the IEEE Transactions in Biomedical Engineerin

A Framework for Uplink Intercell Interference Modeling with Channel-Based Scheduling

This paper presents a novel framework for modeling the uplink intercell interference (ICI) in a multiuser cellular network. The proposed framework assists in quantifying the impact of various fading channel models and state-of-the-art scheduling schemes on the uplink ICI. Firstly, we derive a semianalytical expression for the distribution of the location of the scheduled user in a given cell considering a wide range of scheduling schemes. Based on this, we derive the distribution and moment generating function (MGF) of the uplink ICI considering a single interfering cell. Consequently, we determine the MGF of the cumulative ICI observed from all interfering cells and derive explicit MGF expressions for three typical fading models. Finally, we utilize the obtained expressions to evaluate important network performance metrics such as the outage probability, ergodic capacity, and average fairness numerically. Monte-Carlo simulation results are provided to demonstrate the efficacy of the derived analytical expressions.Comment: IEEE Transactions on Wireless Communications, 2013. arXiv admin note: substantial text overlap with arXiv:1206.229

White Matter Structural Connectivity is Associated with Sensorimotor Function in Stroke Survivors

Purpose Diffusion tensor imaging (DTI) provides functionally relevant information about white matter structure. Local anatomical connectivity information combined with fractional anisotropy (FA) and mean diffusivity (MD) may predict functional outcomes in stroke survivors. Imaging methods for predicting functional outcomes in stroke survivors are not well established. This work uses DTI to objectively assess the effects of a stroke lesion on white matter structure and sensorimotor function. Methods A voxel-based approach is introduced to assess a stroke lesion\u27s global impact on motor function. Anatomical T1-weighted and diffusion tensor images of the brain were acquired for nineteen subjects (10 post-stroke and 9 age-matched controls). A manually selected volume of interest was used to alleviate the effects of stroke lesions on image registration. Images from all subjects were registered to the images of the control subject that was anatomically closest to Talairach space. Each subject\u27s transformed image was uniformly seeded for DTI tractography. Each seed was inversely transformed into the individual subject space, where DTI tractography was conducted and then the results were transformed back to the reference space. A voxel-wise connectivity matrix was constructed from the fibers, which was then used to calculate the number of directly and indirectly connected neighbors of each voxel. A novel voxel-wise indirect structural connectivity (VISC) index was computed as the average number of direct connections to a voxel\u27s indirect neighbors. Voxel-based analyses (VBA) were performed to compare VISC, FA, and MD for the detection of lesion-induced changes in sensorimotor function. For each voxel, a t-value was computed from the differences between each stroke brain and the 9 controls. A series of linear regressions was performed between Fugl-Meyer (FM) assessment scores of sensorimotor impairment and each DTI metric\u27s log number of voxels that differed from the control group. Results Correlation between the logarithm of the number of significant voxels in the ipsilesional hemisphere and total Fugl-Meyer score was moderate for MD (R2 = 0.512), and greater for VISC (R2 = 0.796) and FA (R2 = 0.674). The slopes of FA (p = 0.0036), VISC (p = 0.0005), and MD (p = 0.0199) versus the total FM score were significant. However, these correlations were driven by the upper extremity motor component of the FM score (VISC: R2 = 0.879) with little influence of the lower extremity motor component (FA: R2 = 0.177). Conclusion The results suggest that a voxel-wise metric based on DTI tractography can predict upper extremity sensorimotor function of stroke survivors, and that supraspinal intraconnectivity may have a less dominant role in lower extremity function