Nonlinear Time Series Modeling: A Unified Perspective, Algorithm and Application

Mukhopadhyay, Subhadeep; Parzen, Emanuel

doi:10.3390/jrfm11030037

Cited by 5 publications

(8 citation statements)

References 27 publications

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“…The upper panel of Fig. 1 shows that the "calibrated" background model in (14) as a purple chained line and matches almost exactly the true background density in (11) Fig. 1 provides important insights on the deficiencies of (12) as a candidate background model.…”

Section: Data-driven Corrections For Misspecified Background Modelsmentioning

confidence: 77%

“…Case I: background-only. Let x be a physics sample of n = 1300 observations whose true (unknown) pdf f (x) is equivalent to f b (x) in (11). We set…”

Section: Nonparametric Signal Detectionmentioning

confidence: 99%

“…where f h (x) is the pdf of the unexpected signal and assume its distribution to be normal with center at 37 and width 1.8. Let f b (x) and f s (x) be defined as in (11) and (13), respectively, and let η 1 = 0.15 and η 2 = 0.1. We can start with a nonparametric signal detection stage by setting g(x) = g bs (x) in (30), with f s defined as in (13) dicate a significant departure from the expected backgroundonly model and a prominent peak is observed in correspondence of the signal of interest centered around 25.…”

Section: Semiparametric Signal Characterizationmentioning

confidence: 99%

“…This approach allows the unification of many of the standard results of classical statistics by expressing them in terms of quantiles and comparison distributions and provides a simple and powerful framework for statistical learning and data analysis. The interested reader is directed to [9][10][11][12][13] and references therein, for recent advancements in mode detection, nonparametric time series, goodness-of-fit on prior distributions, and large-scale inference using an LP approach.…”

Section: Introductionmentioning

confidence: 99%

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Detecting new signals under background mismodeling

Algeri

2020

Phys. Rev. D

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Searches for new astrophysical phenomena often involve several sources of non-random uncertainties which can lead to highly misleading results. Among these, model-uncertainty arising from background mismodelling can dramatically compromise the sensitivity of the experiment under study. Specifically, overestimating the background distribution in the signal region increases the chances of missing new physics. Conversely, underestimating the background outside the signal region leads to an artificially enhanced sensitivity and a higher likelihood of claiming false discoveries. The aim of this work is to provide a unified statistical strategy to perform modelling, estimation, inference, and signal characterization under background mismodelling. The method proposed allows to incorporate the (partial) scientific knowledge available on the background distribution and provides a data-updated version of it in a purely nonparametric fashion without requiring the specification of prior distributions. Applications in the context of dark matter searches and radio surveys show how the tools presented in this article can be used to incorporate non-stochastic uncertainty due to instrumental noise and to overcome violations of classical distributional assumptions in stacking experiments.

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Section: Data-driven Corrections For Misspecified Background Modelsmentioning

confidence: 77%

“…Case I: background-only. Let x be a physics sample of n = 1300 observations whose true (unknown) pdf f (x) is equivalent to f b (x) in (11). We set…”

Section: Nonparametric Signal Detectionmentioning

confidence: 99%

Section: Semiparametric Signal Characterizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Detecting new signals under background mismodeling

Algeri

2020

Phys. Rev. D

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“…In particular, {φ k } must be compressible in the new basis, i.e., we need fewer terms (say, m, where m n) in the expansion (2.4) to achieve the target accuracy. One such discrete-orthonormal system (called LP-graph basis) is given below, inspired by the recent work of Mukhopadhyay, Parzen, and their colleague [36][37][38] .…”

Section: Compressive Trial-basis Designmentioning

confidence: 99%

Spectral Graph Analysis: A Unified Explanation and Modern Perspectives

Mukhopadhyay,

Wang

2019

Preprint

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Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful techniques and models for understanding 'patterns of interconnectedness' in a graph. Our prime focus in this paper is on the following question: Is there a unified explanation and description of the fundamental spectral graph methods? There are at least two reasons to be interested in this question. Firstly, to gain a much deeper and refined understanding of the basic foundational principles, and secondly, to derive rich consequences with practical significance for algorithm design. However, despite half a century of research, this question remains one of the most formidable open issues, if not the core problem in modern network science. The achievement of this paper is to take a step towards answering this question by discovering a simple, yet universal statistical logic of spectral graph analysis. The prescribed viewpoint appears to be good enough to accommodate almost all existing spectral graph techniques as a consequence of just one single formalism and algorithm. −1/2 τ A D −1/2 τ Chaudhuri et al. (2012) 6 .

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Nonparametric universal copula modeling

Mukhopadhyay

Parzen

2020

Appl Stoch Models Bus & Ind

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To handle the ubiquitous problem of “dependence learning,” copulas are quickly becoming a pervasive tool across a wide range of data‐driven disciplines encompassing neuroscience, finance, econometrics, genomics, social science, machine learning, healthcare, and many more. At the same time, despite their practical value, the empirical methods of “learning copula from data” have been unsystematic with full of case‐specific recipes. Taking inspiration from modern LP‐nonparametrics, this paper presents a modest contribution to the need for a more unified and structured approach of copula modeling that is simultaneously valid for arbitrary combinations of continuous and discrete variables.

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Nonlinear Time Series Modeling: A Unified Perspective, Algorithm and Application

Cited by 5 publications

References 27 publications

Detecting new signals under background mismodeling

Detecting new signals under background mismodeling

Spectral Graph Analysis: A Unified Explanation and Modern Perspectives

Nonparametric universal copula modeling

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