ترغب بنشر مسار تعليمي؟ اضغط هنا

Direct Nonparametric Predictive Inference Classification Trees

103   0   0.0 ( 0 )
 نشر من قبل Tahani Coolen-Maturi Dr
 تاريخ النشر 2021
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

Classification is the task of assigning a new instance to one of a set of predefined categories based on the attributes of the instance. A classification tree is one of the most commonly used techniques in the area of classification. In this paper, we introduce a novel classification tree algorithm which we call Direct Nonparametric Predictive Inference (D-NPI) classification algorithm. The D-NPI algorithm is completely based on the Nonparametric Predictive Inference (NPI) approach, and it does not use any other assumption or information. The NPI is a statistical methodology which learns from data in the absence of prior knowledge and uses only few modelling assumptions, enabled by the use of lower and upper probabilities to quantify uncertainty. Due to the predictive nature of NPI, it is well suited for classification, as the nature of classification is explicitly predictive as well. The D-NPI algorithm uses a new split criterion called Correct Indication (CI). The CI is about the informativity that the attribute variables will indicate, hence, if the attribute is very informative, it gives high lower and upper probabilities for CI. The CI reports the strength of the evidence that the attribute variables will indicate, based on the data. The CI is completely based on the NPI, and it does not use any additional concepts such as entropy. The performance of the D-NPI classification algorithm is tested against several classification algorithms using classification accuracy, in-sample accuracy and tree size on different datasets from the UCI machine learning repository. The experimental results indicate that the D-NPI classification algorithm performs well in terms of classification accuracy and in-sample accuracy.

قيم البحث

اقرأ أيضاً

Bayesian nonparametric priors based on completely random measures (CRMs) offer a flexible modeling approach when the number of latent components in a dataset is unknown. However, managing the infinite dimensionality of CRMs typically requires practit ioners to derive ad-hoc algorithms, preventing the use of general-purpose inference methods and often leading to long compute times. We propose a general but explicit recipe to construct a simple finite-dimensional approximation that can replace the infinite-dimensional CRMs. Our independent finite approximation (IFA) is a generalization of important cases that are used in practice. The independence of atom weights in our approximation (i) makes the construction well-suited for parallel and distributed computation and (ii) facilitates more convenient inference schemes. We quantify the approximation error between IFAs and the target nonparametric prior. We compare IFAs with an alternative approximation scheme -- truncated finite approximations (TFAs), where the atom weights are constructed sequentially. We prove that, for worst-case choices of observation likelihoods, TFAs are a more efficient approximation than IFAs. However, in real-data experiments with image denoising and topic modeling, we find that IFAs perform very similarly to TFAs in terms of task-specific accuracy metrics.
Many time-to-event studies are complicated by the presence of competing risks. Such data are often analyzed using Cox models for the cause specific hazard function or Fine-Gray models for the subdistribution hazard. In practice regression relationshi ps in competing risks data with either strategy are often complex and may include nonlinear functions of covariates, interactions, high-dimensional parameter spaces and nonproportional cause specific or subdistribution hazards. Model misspecification can lead to poor predictive performance. To address these issues, we propose a novel approach to flexible prediction modeling of competing risks data using Bayesian Additive Regression Trees (BART). We study the simulation performance in two-sample scenarios as well as a complex regression setting, and benchmark its performance against standard regression techniques as well as random survival forests. We illustrate the use of the proposed method on a recently published study of patients undergoing hematopoietic stem cell transplantation.
98 - Yifan Cui , Jan Hannig 2017
Fiducial Inference, introduced by Fisher in the 1930s, has a long history, which at times aroused passionate disagreements. However, its application has been largely confined to relatively simple parametric problems. In this paper, we present what mi ght be the first time fiducial inference, as generalized by Hannig et al. (2016), is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one sample and two sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein-von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test comparing chemotherapy against chemotherapy combined with radiotherapy using data from the treatment of locally unresectable gastric cancer.
Distribution function is essential in statistical inference, and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradig m for statistical inference. However, existing distribution functions are defined in Euclidean spaces and no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the concept of distribution function in a more general space to meet emerging needs. Note that the linearity allows us to use hypercubes to define the distribution function in a Euclidean space, but without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of metric distribution functions through the metric between random objects and a fixed location in metric spaces. We overcome this challenging step by proving the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces that lie the foundation for conducting rational statistical inference for metric space-valued data. Then, we develop homogeneity test and mutual independence test for non-Euclidean random objects, and present comprehensive empirical evidence to support the performance of our proposed methods.
We consider predictive inference using a class of temporally dependent Dirichlet processes driven by Fleming--Viot diffusions, which have a natural bearing in Bayesian nonparametrics and lend the resulting family of random probability measures to ana lytical posterior analysis. Formulating the implied statistical model as a hidden Markov model, we fully describe the predictive distribution induced by these Fleming--Viot-driven dependent Dirichlet processes, for a sequence of observations collected at a certain time given another set of draws collected at several previous times. This is identified as a mixture of Polya urns, whereby the observations can be values from the baseline distribution or copies of previous draws collected at the same time as in the usual P`olya urn, or can be sampled from a random subset of the data collected at previous times. We characterise the time-dependent weights of the mixture which select such subsets and discuss the asymptotic regimes. We describe the induced partition by means of a Chinese restaurant process metaphor with a conveyor belt, whereby new customers who do not sit at an occupied table open a new table by picking a dish either from the baseline distribution or from a time-varying offer available on the conveyor belt. We lay out explicit algorithms for exact and approximate posterior sampling of both observations and partitions, and illustrate our results on predictive problems with synthetic and real data.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا