اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدFrom Data to the p-Adic or Ultrametric Model
41
0
0.0
(
0
)
تأليف
Fionn Murtagh
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We model anomaly and change in data by embedding the data in an ultrametric space. Taking our initial data as cross-tabulation counts (or other input data formats), Correspondence Analysis allows us to endow the information space with a Euclidean metric. We then model anomaly or change by an induced ultrametric. The induced ultrametric that we are particularly interested in takes a sequential - e.g. temporal - ordering of the data into account. We apply this work to the flow of narrative expressed in the film script of the Casablanca movie; and to the evolution between 1988 and 2004 of the Colombian social conflict and violence.
قيم البحث
اقرأ أيضاً
Stochastic variational inference allows for fast posterior inference in complex Bayesian models. However, the algorithm is prone to local optima which can make the quality of the posterior approximation sensitive to the choice of hyperparameters and
initialization. We address this problem by replacing the natural gradient step of stochastic varitional inference with a trust-region update. We show that this leads to generally better results and reduced sensitivity to hyperparameters. We also describe a new strategy for variational inference on streaming data and show that here our trust-region method is crucial for getting good performance.
We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting. We find t
he group of isomorphism classes of character sheaves on $G$ and show that it is an extension of the group of characters of $G(k)$ by a cohomology group determined by the component group scheme of $G$. We also classify all morphisms in the category character sheaves on $G$. As an application, we study character sheaves on Greenberg transforms of locally finite type Neron models of algebraic tori over local fields. This provides a geometrization of quasicharacters of $p$-adic tori.
Beta regression has been extensively used by statisticians and practitioners to model bounded continuous data and there is no strong and similar competitor having its main features. A class of normalized inverse-Gaussian (N-IG) process was introduced
in the literature, being explored in the Bayesian context as a powerful alternative to the Dirichlet process. Until this moment, no attention has been paid for the univariate N-IG distribution in the classical inference. In this paper, we propose the bessel regression based on the univariate N-IG distribution, which is a robust alternative to the beta model. This robustness is illustrated through simulated and real data applications. The estimation of the parameters is done through an Expectation-Maximization algorithm and the paper discusses how to perform inference. A useful and practical discrimination procedure is proposed for model selection between bessel and beta regressions. Monte Carlo simulation results are presented to verify the finite-sample behavior of the EM-based estimators and the discrimination procedure. Further, the performances of the regressions are evaluated under misspecification, which is a critical point showing the robustness of the proposed model. Finally, three empirical illustrations are explored to confront results from bessel and beta regressions.
Instrumental variables (IVs) are extensively used to estimate treatment effects when the treatment and outcome are confounded by unmeasured confounders; however, weak IVs are often encountered in empirical studies and may cause problems. Many studies
have considered building a stronger IV from the original, possibly weak, IV in the design stage of a matched study at the cost of not using some of the samples in the analysis. It is widely accepted that strengthening an IV tends to render nonparametric tests more powerful and will increase the power of sensitivity analyses in large samples. In this article, we re-evaluate this conventional wisdom to bring new insights into this topic. We consider matched observational studies from three perspectives. First, we evaluate the trade-off between IV strength and sample size on nonparametric tests assuming the IV is valid and exhibit conditions under which strengthening an IV increases power and conversely conditions under which it decreases power. Second, we derive a necessary condition for a valid sensitivity analysis model with continuous doses. We show that the $Gamma$ sensitivity analysis model, which has been previously used to come to the conclusion that strengthening an IV increases the power of sensitivity analyses in large samples, does not apply to the continuous IV setting and thus this previously reached conclusion may be invalid. Third, we quantify the bias of the Wald estimator with a possibly invalid IV under an oracle and leverage it to develop a valid sensitivity analysis framework; under this framework, we show that strengthening an IV may amplify or mitigate the bias of the estimator, and may or may not increase the power of sensitivity analyses. We also discuss how to better adjust for the observed covariates when building an IV in matched studies.
We study $p$-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating a MRA (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all suc
h scaling functions generate Haar MRA. We also suggest a method of constructing sets of wavelet functions and prove that any set of wavelet functions generates a $p$-adic wavelet frame.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
