14,485 research outputs found
On rate optimal private regression under local differential privacy
We consider the problem of estimating a regression function from anonymized
data in the framework of local differential privacy. We propose a novel
partitioning estimate of the regression function, derive a rate of convergence
for the excess prediction risk over H\"older classes, and prove a matching
lower bound. In contrast to the existing literature on the problem the
so-called strong density assumption on the design distribution is obsolete.Comment: Revised versio
Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio
This paper reviews the most common situations where one or more regularity
conditions which underlie classical likelihood-based parametric inference fail.
We identify three main classes of problems: boundary problems, indeterminate
parameter problems -- which include non-identifiable parameters and singular
information matrices -- and change-point problems. The review focuses on the
large-sample properties of the likelihood ratio statistic. We emphasize
analytical solutions and acknowledge software implementations where available.
We furthermore give summary insight about the possible tools to derivate the
key results. Other approaches to hypothesis testing and connections to
estimation are listed in the annotated bibliography of the Supplementary
Material
Subsidiary Entrepreneurial Alertness: Antecedents and Outcomes
This thesis brings together concepts from both international business and entrepreneurship to develop a framework of the facilitators of subsidiary innovation and performance. This study proposes that Subsidiary Entrepreneurial Alertness (SEA) facilitates the recognition of opportunities (the origin of subsidiary initiatives). First introduced by Kirzner (1979) in the context of the individual, entrepreneurial alertness (EA) is the ability to notice an opportunity without actively searching. Similarly, to entrepreneurial alertness at the individual level, this study argues that SEA enables the subsidiary to best select opportunities based on resources available. The research further develops our conceptualisation of SEA by drawing on work by Tang et al. (2012) identifying three distinct activities of EA: scanning and search (identifying opportunities unseen by others due to their awareness gaps), association and connection of information, and evaluation and judgement to interpret or anticipate future viability of opportunities. This study then hypothesises that SEA leads to opportunity recognition at the subsidiary level and further hypothesises innovation and performance as outcomes of opportunity recognition. This research brings these arguments together to develop and test a comprehensive theoretical model.
The theoretical model is tested through a mail survey of the CEOs/MDs of foreign subsidiaries within the Republic of Ireland (an innovative hub for foreign subsidiaries). This method was selected as the best method to reach the targeted respondent, and due to the depth of knowledge the target respondent holds, the survey can answer the desired question more substantially. The results were examined using partial least squares structural equation modelling (PLS-SEM). The study’s findings confirm two critical aspects of subsidiary context, subsidiary brokerage and subsidiary credibility are positively related to SEA. The study establishes a positive link between SEA and both the generation of innovation and the subsidiary’s performance. This thesis makes three significant contributions to the subsidiary literature as it 1) introduces and develops the concept of SEA, 2) identifies the antecedents of SEA, and 3) demonstrates the impact of SEA on subsidiary opportunity recognition. Implications for subsidiaries, headquarters and policy makers are discussed along with the limitations of the study
Global Convergence of SGD On Two Layer Neural Nets
In this note we demonstrate provable convergence of SGD to the global minima
of appropriately regularized empirical risk of depth nets -- for
arbitrary data and with any number of gates, if they are using adequately
smooth and bounded activations like sigmoid and tanh. We build on the results
in [1] and leverage a constant amount of Frobenius norm regularization on the
weights, along with sampling of the initial weights from an appropriate
distribution. We also give a continuous time SGD convergence result that also
applies to smooth unbounded activations like SoftPlus. Our key idea is to show
the existence loss functions on constant sized neural nets which are "Villani
Functions". [1] Bin Shi, Weijie J. Su, and Michael I. Jordan. On learning rates
and schr\"odinger operators, 2020. arXiv:2004.06977Comment: 23 pages, 6 figures. Extended abstract accepted at DeepMath 2022. v2
update: New experiments added in Section 3.2 to study the effect of the
regularization value. Statement of Theorem 3.4 about SoftPlus nets has been
improve
On Monte Carlo methods for the Dirichlet process mixture model, and the selection of its precision parameter prior
Two issues commonly faced by users of Dirichlet process mixture models are: 1) how to appropriately select a hyperprior for its precision parameter alpha, and 2) the typically slow mixing of the MCMC chain produced by conditional Gibbs samplers based on its stick-breaking representation, as opposed to marginal collapsed Gibbs samplers based on the Polya urn, which have smaller integrated autocorrelation times.
In this thesis, we analyse the most common approaches to hyperprior selection for alpha, we identify their limitations, and we propose a new methodology to overcome them.
To address slow mixing, we revisit three label-switching Metropolis moves from the literature (Hastie et al., 2015; Papaspiliopoulos and Roberts, 2008), improve them, and introduce a fourth move. Secondly, we revisit two i.i.d. sequential importance samplers which operate in the collapsed space (Liu, 1996; S. N. MacEachern et al., 1999), and we develop a new sequential importance sampler for the stick-breaking parameters of Dirichlet process mixtures, which operates in the stick-breaking space and which has minimal integrated autocorrelation time. Thirdly, we introduce the i.i.d. transcoding algorithm which, conditional to a partition of the data, can infer back which specific stick in the stick-breaking construction each observation originated from. We use it as a building block to develop the transcoding sampler, which removes the need for label-switching Metropolis moves in the conditional stick-breaking sampler, as it uses the better performing marginal sampler (or any other sampler) to drive the MCMC chain, and augments its exchangeable partition posterior with conditional i.i.d. stick-breaking parameter inferences after the fact, thereby inheriting its shorter autocorrelation times
Genomic prediction in plants: opportunities for ensemble machine learning based approaches [version 2; peer review: 1 approved, 2 approved with reservations]
Background: Many studies have demonstrated the utility of machine learning (ML) methods for genomic prediction (GP) of various plant traits, but a clear rationale for choosing ML over conventionally used, often simpler parametric methods, is still lacking. Predictive performance of GP models might depend on a plethora of factors including sample size, number of markers, population structure and genetic architecture. Methods: Here, we investigate which problem and dataset characteristics are related to good performance of ML methods for genomic prediction. We compare the predictive performance of two frequently used ensemble ML methods (Random Forest and Extreme Gradient Boosting) with parametric methods including genomic best linear unbiased prediction (GBLUP), reproducing kernel Hilbert space regression (RKHS), BayesA and BayesB. To explore problem characteristics, we use simulated and real plant traits under different genetic complexity levels determined by the number of Quantitative Trait Loci (QTLs), heritability (h2 and h2e), population structure and linkage disequilibrium between causal nucleotides and other SNPs. Results: Decision tree based ensemble ML methods are a better choice for nonlinear phenotypes and are comparable to Bayesian methods for linear phenotypes in the case of large effect Quantitative Trait Nucleotides (QTNs). Furthermore, we find that ML methods are susceptible to confounding due to population structure but less sensitive to low linkage disequilibrium than linear parametric methods. Conclusions: Overall, this provides insights into the role of ML in GP as well as guidelines for practitioners
Nonparametric Two-Sample Test for Networks Using Joint Graphon Estimation
This paper focuses on the comparison of networks on the basis of statistical
inference. For that purpose, we rely on smooth graphon models as a
nonparametric modeling strategy that is able to capture complex structural
patterns. The graphon itself can be viewed more broadly as density or intensity
function on networks, making the model a natural choice for comparison
purposes. Extending graphon estimation towards modeling multiple networks
simultaneously consequently provides substantial information about the
(dis-)similarity between networks. Fitting such a joint model - which can be
accomplished by applying an EM-type algorithm - provides a joint graphon
estimate plus a corresponding prediction of the node positions for each
network. In particular, it entails a generalized network alignment, where
nearby nodes play similar structural roles in their respective domains. Given
that, we construct a chi-squared test on equivalence of network structures.
Simulation studies and real-world examples support the applicability of our
network comparison strategy.Comment: 25 pages, 6 figure
Structured Dynamic Pricing: Optimal Regret in a Global Shrinkage Model
We consider dynamic pricing strategies in a streamed longitudinal data set-up
where the objective is to maximize, over time, the cumulative profit across a
large number of customer segments. We consider a dynamic probit model with the
consumers' preferences as well as price sensitivity varying over time. Building
on the well-known finding that consumers sharing similar characteristics act in
similar ways, we consider a global shrinkage structure, which assumes that the
consumers' preferences across the different segments can be well approximated
by a spatial autoregressive (SAR) model. In such a streamed longitudinal
set-up, we measure the performance of a dynamic pricing policy via regret,
which is the expected revenue loss compared to a clairvoyant that knows the
sequence of model parameters in advance. We propose a pricing policy based on
penalized stochastic gradient descent (PSGD) and explicitly characterize its
regret as functions of time, the temporal variability in the model parameters
as well as the strength of the auto-correlation network structure spanning the
varied customer segments. Our regret analysis results not only demonstrate
asymptotic optimality of the proposed policy but also show that for policy
planning it is essential to incorporate available structural information as
policies based on unshrunken models are highly sub-optimal in the
aforementioned set-up.Comment: 34 pages, 5 figure
Examples of works to practice staccato technique in clarinet instrument
Klarnetin staccato tekniğini güçlendirme aşamaları eser çalışmalarıyla uygulanmıştır. Staccato
geçişlerini hızlandıracak ritim ve nüans çalışmalarına yer verilmiştir. Çalışmanın en önemli amacı
sadece staccato çalışması değil parmak-dilin eş zamanlı uyumunun hassasiyeti üzerinde de
durulmasıdır. Staccato çalışmalarını daha verimli hale getirmek için eser çalışmasının içinde etüt
çalışmasına da yer verilmiştir. Çalışmaların üzerinde titizlikle durulması staccato çalışmasının ilham
verici etkisi ile müzikal kimliğe yeni bir boyut kazandırmıştır. Sekiz özgün eser çalışmasının her
aşaması anlatılmıştır. Her aşamanın bir sonraki performans ve tekniği güçlendirmesi esas alınmıştır.
Bu çalışmada staccato tekniğinin hangi alanlarda kullanıldığı, nasıl sonuçlar elde edildiği bilgisine
yer verilmiştir. Notaların parmak ve dil uyumu ile nasıl şekilleneceği ve nasıl bir çalışma disiplini
içinde gerçekleşeceği planlanmıştır. Kamış-nota-diyafram-parmak-dil-nüans ve disiplin
kavramlarının staccato tekniğinde ayrılmaz bir bütün olduğu saptanmıştır. Araştırmada literatür
taraması yapılarak staccato ile ilgili çalışmalar taranmıştır. Tarama sonucunda klarnet tekniğin de
kullanılan staccato eser çalışmasının az olduğu tespit edilmiştir. Metot taramasında da etüt
çalışmasının daha çok olduğu saptanmıştır. Böylelikle klarnetin staccato tekniğini hızlandırma ve
güçlendirme çalışmaları sunulmuştur. Staccato etüt çalışmaları yapılırken, araya eser çalışmasının
girmesi beyni rahatlattığı ve istekliliği daha arttırdığı gözlemlenmiştir. Staccato çalışmasını yaparken
doğru bir kamış seçimi üzerinde de durulmuştur. Staccato tekniğini doğru çalışmak için doğru bir
kamışın dil hızını arttırdığı saptanmıştır. Doğru bir kamış seçimi kamıştan rahat ses çıkmasına
bağlıdır. Kamış, dil atma gücünü vermiyorsa daha doğru bir kamış seçiminin yapılması gerekliliği
vurgulanmıştır. Staccato çalışmalarında baştan sona bir eseri yorumlamak zor olabilir. Bu açıdan
çalışma, verilen müzikal nüanslara uymanın, dil atış performansını rahatlattığını ortaya koymuştur.
Gelecek nesillere edinilen bilgi ve birikimlerin aktarılması ve geliştirici olması teşvik edilmiştir.
Çıkacak eserlerin nasıl çözüleceği, staccato tekniğinin nasıl üstesinden gelinebileceği anlatılmıştır.
Staccato tekniğinin daha kısa sürede çözüme kavuşturulması amaç edinilmiştir. Parmakların
yerlerini öğrettiğimiz kadar belleğimize de çalışmaların kaydedilmesi önemlidir. Gösterilen azmin ve
sabrın sonucu olarak ortaya çıkan yapıt başarıyı daha da yukarı seviyelere çıkaracaktır
- …