Extra‐binomial variation in multilevel logistic models with sparse structures

BackgroundAutomated feature selection methods such as the Least Absolute Shrinkage and Selection Operator (LASSO) have recently gained importance in the prediction of quality-related outcomes as well as the risk-adjustment of quality indicators in healthcare. The methods that have been used so far, however, do not account for the fact that patient data are typically nested within hospitals.MethodsTherefore, we aimed to demonstrate how to account for the multilevel structure of hospital data with LASSO and compare the results of this procedure with a LASSO variant that ignores the multilevel structure of the data. We used three different data sets (from acute myocardial infarcation, COPD, and stroke patients) with two dependent variables (one numeric and one binary), on which different LASSO variants with and without consideration of the nested data structure were applied. Using a 20-fold sub-sampling procedure, we tested the predictive performance of the different LASSO variants and examined differences in variable importance.ResultsFor the metric dependent variable Duration Stay, we found that inserting hospitals led to better predictions, whereas for the binary variable Mortality, all methods performed equally well. However, in some instances, the variable importances differed greatly between the methods.ConclusionWe showed that it is possible to take the multilevel structure of data into account in automated predictor selection and that this leads, at least partly, to better predictive performance. From the perspective of variable importance, including the multilevel structure is crucial to select predictors in an unbiased way under consideration of the structural differences between hospitals.

Multilevel data and Bayesian analysis in traffic safety

The concepts of sparse data structures and related algorithms for phase field simulations are discussed. Simulations of polycrystalline grain growth with a conventional phase field method and with sparse data structures are compared. It is shown that memory usage and simulation time scale with the number of nodes but are independent of the number of order parameters when a sparse data structure is used.

Multilevel data structures are those that have a hierarchical structure, in which response variables are measured at the lowest level of the hierarchy and modeled as a function of predictor variables measured at that level and higher levels of the hierarchy. For example, a multilevel data structure may consist of measurements taken on individual fish (lower level) that are nested within lakes or streams (higher level). Multilevel data structures are a common feature in fisheries research. We provide simulated fisheries data examples, similar in structure to other published studies, to illustrate the application of multilevel models and discuss how hypothesis testing and inferences can be incorrect if multilevel data structures are ignored. Ignoring multilevel data structures has implications for the use of commonly-used ordinary least squares (OLS) approaches to test hypotheses and to make inferences. Multilevel models are an alternate approach that circumvents problems associated with traditional OLS methods and allows valid inferences to be made.

The statistical analysis of a thurstonian model for rating chess players

Sparse and low-rank methods in structural system identification and monitoring

The paper describes graph algorithms performance when using different types of data structures. To achieve that, we developed a multi-level graph processing system, which allows to create graph applications independently of any implementation details such as graph data structure or underlying computational architecture. We measure the performance of breadth-first search, max flow and random graph building algorithms when using compressed sparse row and adjacency matrix data structures. Experiments reveal different graph processing rates for different data structures, which indicates the need of using specific data structures for specific algorithms to achieve highest performance.

We have developed a novel hierarchical data structure for the efficient representation of sparse, time-varying volumetric data discretized on a 3D grid. Our “VDB”, so named because it is a Volumetric, Dynamic grid that shares several characteristics with B+trees, exploits spatial coherency of time-varying data to separately and compactly encode data values and grid topology. VDB models a virtually infinite 3D index space that allows for cache-coherent and fast data access into sparse volumes of high resolution. It imposes no topology restrictions on the sparsity of the volumetric data, and it supports fast (average O (1)) random access patterns when the data are inserted, retrieved, or deleted. This is in contrast to most existing sparse volumetric data structures, which assume either static or manifold topology and require specific data access patterns to compensate for slow random access. Since the VDB data structure is fundamentally hierarchical, it also facilitates adaptive grid sampling, and the inherent acceleration structure leads to fast algorithms that are well-suited for simulations. As such, VDB has proven useful for several applications that call for large, sparse, animated volumes, for example, level set dynamics and cloud modeling. In this article, we showcase some of these algorithms and compare VDB with existing, state-of-the-art data structures.

Multilevel data structures are known as consisting of multiple units of analysis, one clustered within the other. The concept of multilevel data modelling has been developed for several years mainly because the researchers have realized the disadvantages of ignoring such multilevel data structures. This study aims to find out factors affecting the General Certificate of Education Ordinary Level (G.C.E. O/L) pass rate at schools located in civil war affected provinces in Sri Lanka. The study also extends to observe the multilevel data structure by schools, districts and provinces, and determine how these levels have an impact on the G.C.E. O/L pass rate. The above has been undertaken by the application of advanced analysis focused on developing Generalized Linear Multilevel Model for ordered categorical response using the Bayesian Markov Chain Monte Carlo estimation method employing MLwiN 2.10 software. Finally, the partial non-proportional odds model was selected as the most appropriate model for the Educational data used in this study based on account of its simplicity and accuracy.

At the core of any inference procedure, deep neural networks are dot product operations, which are the component that requires the highest computational resources. For instance, deep neural networks, such as VGG-16, require up to 15-G operations in order to perform the dot products present in a single forward pass, which results in significant energy consumption and thus limits their use in resource-limited environments, e.g., on embedded devices or smartphones. One common approach to reduce the complexity of the inference is to prune and quantize the weight matrices of the neural network. Usually, this results in matrices whose entropy values are low, as measured relative to the empirical probability mass distribution of its elements. In order to efficiently exploit such matrices, one usually relies on, inter alia, sparse matrix representations. However, most of these common matrix storage formats make strong statistical assumptions about the distribution of the elements; therefore, cannot efficiently represent the entire set of matrices that exhibit low-entropy statistics (thus, the entire set of compressed neural network weight matrices). In this paper, we address this issue and present new efficient representations for matrices with low-entropy statistics. Alike sparse matrix data structures, these formats exploit the statistical properties of the data in order to reduce the size and execution complexity. Moreover, we show that the proposed data structures can not only be regarded as a generalization of sparse formats but are also more energy and time efficient under practically relevant assumptions. Finally, we test the storage requirements and execution performance of the proposed formats on compressed neural networks and compare them to dense and sparse representations. We experimentally show that we are able to attain up to ×42 compression ratios, ×5 speed ups, and ×90 energy savings when we lossless convert the state-of-the-art networks, such as AlexNet, VGG-16, ResNet152, and DenseNet, into the new data structures and benchmark their respective dot product.

We present a framework for compiling recurrence equations into native code. In our framework, users specify a system of recurrences, the types of data structures that store inputs and outputs, and scheduling commands for optimization. Our compiler then lowers these specifications into native code that respects the dependencies in the recurrence equations. Our compiler can generate code over both sparse and dense data structures, and determines if the recurrence system is solvable with the provided scheduling primitives. We evaluate the performance and correctness of the generated code on several recurrences, from domains as diverse as dense and sparse matrix solvers, dynamic programming, graph problems, and sparse tensor algebra. We demonstrate that the generated code has competitive performance to hand-optimized implementations in libraries. However, these handwritten libraries target specific recurrences, specific data structures, and specific optimizations. Our system, on the other hand, automatically generates implementations from recurrences, data formats, and schedules, giving our system more generality than library approaches.

To construct CFA, MCFA, and maximum MCFA with LISREL v.8 and below, we provide iMCFA (integrated Multilevel Confirmatory Analysis) to examine the potential multilevel factorial structure in the complex survey data. Modeling multilevel structure for complex survey data is complicated because building a multilevel model is not an infallible statistical strategy unless the hypothesized model is close to the real data structure. Methodologists have suggested using different modeling techniques to investigate potential multilevel structure of survey data. Using iMCFA, researchers can visually set the between- and within-level factorial structure to fit MCFA, CFA and/or MAX MCFA models for complex survey data. iMCFA can then yield between- and within-level variance-covariance matrices, calculate intraclass correlations, perform the analyses and generate the outputs for respective models. The summary of the analytical outputs from LISREL is gathered and tabulated for further model comparison and interpretation. iMCFA also provides LISREL syntax of different models for researchers' future use. An empirical and a simulated multilevel dataset with complex and simple structures in the within or between level was used to illustrate the usability and the effectiveness of the iMCFA procedure on analyzing complex survey data. The analytic results of iMCFA using Muthen's limited information estimator were compared with those of Mplus using Full Information Maximum Likelihood regarding the effectiveness of different estimation methods.

In this paper, we consider several efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular the maximum and minimum rate, and where the number of possible outcomes N is large. We consider three basic data structures, the Acceptance–Rejection method, the Complete Binary Tree and the Alias method. These can be used as building blocks in a multi-level data structure, where at each of the levels, one of the basic data structures can be used, with the top level selecting a group of events, and the bottom level selecting an element from a group. Depending on assumptions on the distribution of the rates of outcomes, different combinations of the basic structures can be used. We prove that for particular data structures the expected time of sampling and update is constant when the rate distribution follows certain conditions. We show that for any distribution, combining a tree structure with the Acceptance–Rejection method, we have an expected time of sampling and update of Oleft( log log {r_{max}}/{r_{min}}right) is possible, where r_{max} is the maximum rate and r_{min} the minimum rate. We also discuss an implementation of a Two Levels Acceptance–Rejection data structure, that allows expected constant time for sampling, and amortized constant time for updates, assuming that r_{max} and r_{min} are known and the number of events is sufficiently large. We also present an experimental verification, highlighting the limits given by the constraints of a real-life setting.

Sparse regularization discriminant analysis for face recognition

Coalition research increasingly emphasizes party-level explanations of coalition outcomes. However, this work does not account for the complex multilevel structure between parties and governments: many parties participate in multiple governments and governments often comprise multiple parties. In this paper, I show that this crisscrossing structure creates dependencies among observations both across and within governments. If ignored, these dependencies produce downward-biased uncertainty estimates that cluster-robust standard errors fail to fully correct. To address this issue, I then introduce a model that extends the Multiple Membership Multilevel Model to represent the multilevel structure of coalition government data. The model accounts for party-level dependencies across governments through party-specific effects in each coalition they join, and for dependencies within governments by representing the total party effect on a government as a weighted sum of its members’ contributions. By allowing party weights to vary with covariates describing their interrelationships, the model enables researchers to examine the interdependent nature of coalition outcomes. I validate the model through simulation and an empirical application to coalition government survival, showing that ignoring party-level dependencies can produce misleading conclusions at all levels of analysis. The model is estimated via Bayesian MCMC and implemented in the accompanying R package ‘bml’.