Product-form estimators: exploiting independence to scale up Monte Carlo

We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target’s independence structure. We identify the most basic incarnations of these estimators with a class of generalized U-statistics and thus establish their unbiasedness, consistency, and asymptotic normality. Moreover, we show that they obtain the minimum possible variance amongst a broad class of estimators, and we investigate their computational cost and delineate the settings in which they are most efficient. We exemplify the merger of these estimators with other well known Monte Carlo estimators so as to better adapt the latter to the target’s independence structure and improve their performance. We do this via three simple mergers: one with importance sampling, another with importance sampling squared, and a final one with pseudo-marginal Metropolis–Hastings. In all cases, we show that the resulting estimators are well founded and achieve lower variances than their standard counterparts. Lastly, we illustrate the various variance reductions through several examples.

Learning social networks from text data using covariate information

Accurately describing the lives of historical figures can be challenging, but unraveling their social structures perhaps is even more so. Historical social network analysis methods can help in this regard and may even illuminate individuals who have been overlooked by historians, but turn out to be influential social connection points. Text data, such as biographies, are a useful source of information for learning historical social networks but the identifcation of links based on text data can be challenging. The Local Poisson Graphical Lasso model models social networks by conditional independence structures, and leverages the number of name co-mentions in the text to infer relationships. However, this method does not take into account the abundance of covariate information that is often available in text data. Conditional independence structure like Poisson Graphical Model, which makes use name mention counts in the text can be useful tools to avoid false positive links due to the co-mentions but given historical tendency of frequently used or common names, without additional distinguishing information, we may introduce incorrect connections. In this work, we therefore extend the Local Poisson Graphical Lasso model with a (multiple) penalty structure that incorporates covariates, opening up the opportunity for similar individuals to have a higher probability of being connected. We propose both greedy and Bayesian approaches to estimate the penalty parameters. We present results on data simulated with characteristics of historical networks and show that this type of penalty structure can improve network recovery as measured by precision and recall. We also illustrate the approach on biographical data of individuals who lived in early modern Britain between 1500 and 1575. We will show how these covariates affect the statistical model’s performance using simulations, discuss how it helps to better identify links for the people with common names and those who are traditionally underrepresented in the biography text data.

Jewel: A Novel Method for Joint Estimation of Gaussian Graphical Models

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix’s symmetry and the graphs’ joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator’s consistency property. Finally, we illustrate our estimator’s performance through simulated and real data examples on gene regulatory networks.

Hardness of Learning in Rich Environments and Some Consequences for Financial Markets

This paper examines the computational feasibility of the standard model of learning in economic theory. It is shown that the information update technique at the heart of this model is impossible to compute in all but the simplest scenarios. Specifically, using tools from theoretical machine learning, the paper first demonstrates that there is no polynomial implementation of the model unless the independence structure of variables in the data is publicly known. Next, it is shown that there cannot exist a polynomial algorithm to infer the independence structure; consequently, the overall learning problem does not have a polynomial implementation. Using the learning model when it is computationally infeasible carries risks, and some of these are explored in the latter part of the paper in the context of financial markets. Especially in rich, high-frequency environments, it implies discarding a lot of useful information, and this can lead to paradoxical outcomes in interactive game-theoretic situations. This is illustrated in a trading example where market prices can never reflect an informed trader’s information, no matter how many rounds of trade. The paper provides new theoretical motivation for the use of bounded rationality models in the study of financial asset pricing—the bound on rationality arising from the computational hardness in learning.

Weak equivalence of higher-dimensional automata

This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence structure of an HDA. It is shown that weak equivalence is compatible with both the tensor product and the coproduct of HDAs and that, under certain conditions, HDAs may be reduced to weakly equivalent smaller ones by merging and collapsing cubes.

Marginal quantile regression for longitudinal data analysis in the presence of time-dependent covariates

When observations are correlated, modeling the within-subject correlation structure using quantile regression for longitudinal data can be difficult unless a working independence structure is utilized. Although this approach ensures consistent estimators of the regression coefficients, it may result in less efficient regression parameter estimation when data are highly correlated. Therefore, several marginal quantile regression methods have been proposed to improve parameter estimation. In a longitudinal study some of the covariates may change their values over time, and the topic of time-dependent covariate has not been explored in the marginal quantile literature. As a result, we propose an approach for marginal quantile regression in the presence of time-dependent covariates, which includes a strategy to select a working type of time-dependency. In this manuscript, we demonstrate that our proposed method has the potential to improve power relative to the independence estimating equations approach due to the reduction of mean squared error.

Regularized Within-Class Precision Matrix Based PLDA in Text-Dependent Speaker Verification

In the field of speaker verification, probabilistic linear discriminant analysis (PLDA) is the dominant method for back-end scoring. To estimate the PLDA model, the between-class covariance and within-class precision matrices must be estimated from samples. However, the empirical covariance/precision estimated from samples has estimation errors due to the limited number of samples available. In this paper, we propose a method to improve the conventional PLDA by estimating the PLDA model using the regularized within-class precision matrix. We use graphical least absolute shrinking and selection operator (GLASSO) for the regularization. The GLASSO regularization decreases the estimation errors in the empirical precision matrix by making the precision matrix sparse, which corresponds to the reflection of the conditional independence structure. The experimental results on text-dependent speaker verification reveal that the proposed method reduce the relative equal error rate by up to 23% compared with the conventional PLDA.

REVITALISASI BADAN WAKAF INDONESIA (BWI) ANALISIS KRITIS UNDANG-UNDANG NOMOR 41 TAHUN 2004 TENTANG WAKAF

This study aims to illustrate how the existence and position of Badan Wakaf Indonesia according to Law Number 41 of 2004 concerning Waqf, will then be studied more deeply to find out how to revitalize the status, roles and responsibilities of Badan Wakaf Indonesia in managing waqf in Indonesia in the context of management endowments that are effective and effective. The establishment of Badan Wakaf Indonesia (BWI) is a consequence of the issuance of Law No. 41 of 2004 concerning Waqf so that Badan Wakaf Indonesia has a strong legal position in the structure of national law. However, in the legal construction of the authority, duties and responsibilities of Badan Wakaf Indonesia there are several shortcomings, namely related to the status, independence, structure, duties and funding of this institution, which has a very significant effect on the implementation, management and development of endowments in Indonesia. Therefore, one of the ways to revitalize the status, roles and responsibilities of the Indonesian Waqf Agency in waqf regulation is to improve the institutional status of Badan Wakaf Indonesia to become a Nonstructural Government Institution (LNS) so that it becomes clear in the constitutional system which is directly under the President and can budgeting for their own funds charged to the state budget, the institutional status can be equated with the National Zakat Amil Agency (BAZNAS).Keywords: Revitalization, Badan Wakaf Indonesia, Endowments.AbstrakPenelitian ini bertujuan untuk memberikan gambaran bagaimana eksistensi dan kedudukan Badan Wakaf Indonesia menurut Undang-Undang Nomor 41 Tahun 2004 tentang Wakaf, kemudian akan dikaji lebih dalam untuk menemukan bagaimana merevitalisasi status, peran dan tanggung jawab Badan Wakaf Indonesia dalam pengelolaan wakaf di Indonesia dalam konteks pengelolaan wakaf yang berdaya guna dan berhasil guna. Dibentuknya Badan Wakaf Indonesia (BWI) merupakan konsekuensi dari lahirnya Undang-Undang Nomor 41 Tahun 2004 tentang Wakaf sehingga Badan Wakaf Indonesia mempunyai kedudukan hukum yang kuat dalam struktur hukum nasional. Namun dalam konstruksi hukum tentang wewenang, tugas dan tanggungjawab Badan Wakaf Indonesia terdapat beberapa kekurangan, yaitu terkait dengan status, independensi, struktur, tugas dan pembiayaan lembaga ini, yang mana hal tersebut berpengaruh sangat signifikan terhadap pelaksanaan, pengelolaan dan pengembangan perwakafan di Indonesia. Oleh karena itu, salah satu langkah merevitalisasi status, peran dan tanggung jawab Badan Wakaf Indonesia dalam regulasi wakaf adalah dengan meningkatkan status kelembagaan Badan Wakaf Indonesia menjadi Lembaga Pemerintah Nonstruktural (LNS) sehingga menjadi jelas dalam sistem ketatanegaraan yang mana kedudukannya langsung berada di bawah Presiden dan dapat menganggarkan sendiri pembiayaannya yang dibebankan kepada APBN, status kelembagaan tersebut dapat disamakan dengan Badan Amil Zakat Nasional (BAZNAS).Kata kunci: Revitalisasi, Badan Wakaf Indonesia, Wakaf

Characteristics and Temporal Behavior of Internet Backbone Traffic

With the rapid increase demand for data usage, Internet has become complex and harder to analyze. Characterizing the Internet traffic might reveal information that are important for Network Operators to formulate policy decisions, develop techniques to detect network anomalies, help better provision network resources (capacity, buffers) and use workload characteristics for simulations (typical packet sizes, flow durations, common protocols). In this paper, using passive monitoring and measurements, we show collected data traffic at Internet backbone routers. First, we reveal main observations on patterns and characteristics of this dataset including packet sizes, traffic volume for inter and intra domain and protocol composition. Second, we further investigate independence structure of packet size arrivals using both visual and computational statistics. Finally, we show the temporal behavior of most active destination IP and Port addresses.

On the Graphicity of the Independence Structure of Linear Active Networks

Consider a linear network composed of 2-terminal devices. Its interconnection structure is described by a graph G. The voltages or the currents of a subset of devices can independently be prescribed if and only if the subset of the corresponding edges in the graph G is circuit-free or cut set free, respectively. This classical result of Kirchhoff can be generalized for networks containing multiterminal devices as well: the independence structure can be described by the circuits and cut sets of a more general abstract mathematical structure, a matroid M. However, these matroids will not always be graphic. Using some recent mathematical results for characterizing graphic structures among the matroids, here we give a physical characterization of subclasses of those active networks where M happens to be graphic.