124,256 research outputs found
Statistical inference and data mining: false discoveries control
Data Mining is characterised by its ability at processing large amounts of data. Among those are the data ”features”- variables or association rules that can be derived from them. Selecting the most interesting features is a classical data mining problem. That selection requires a large number of tests from which arise a number of false discoveries. An original non parametric control method is proposed in this paper. A new criterion, UAFWER, defined as the risk of exceeding a pre-set number of false discoveries, is controlled by BS FD, a bootstrap based algorithm that can be used on one- or two-sided problems. The usefulness of the procedure is illustrated by the selection of differentially interesting association rules on genetic data
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
Data envelopment analysis and data mining to efficiency estimation and evaluation
Purpose: This paper aims to assess the application of seven statistical and data mining techniques to second-stage data envelopment analysis (DEA) for bank performance. Design/methodology/approach: Different statistical and data mining techniques are used to second-stage DEA for bank performance as a part of an attempt to produce a powerful model for bank performance with effective predictive ability. The projected data mining tools are classification and regression trees (CART), conditional inference trees (CIT), random forest based on CART and CIT, bagging, artificial neural networks and their statistical counterpart, logistic regression. Findings: The results showed that random forests and bagging outperform other methods in terms of predictive power. Originality/value: This is the first study to assess the impact of environmental factors on banking performance in Middle East and North Africa countries.Scopu
Phase Transitions in Semidefinite Relaxations
Statistical inference problems arising within signal processing, data mining,
and machine learning naturally give rise to hard combinatorial optimization
problems. These problems become intractable when the dimensionality of the data
is large, as is often the case for modern datasets. A popular idea is to
construct convex relaxations of these combinatorial problems, which can be
solved efficiently for large scale datasets.
Semidefinite programming (SDP) relaxations are among the most powerful
methods in this family, and are surprisingly well-suited for a broad range of
problems where data take the form of matrices or graphs. It has been observed
several times that, when the `statistical noise' is small enough, SDP
relaxations correctly detect the underlying combinatorial structures.
In this paper we develop asymptotic predictions for several `detection
thresholds,' as well as for the estimation error above these thresholds. We
study some classical SDP relaxations for statistical problems motivated by
graph synchronization and community detection in networks. We map these
optimization problems to statistical mechanics models with vector spins, and
use non-rigorous techniques from statistical mechanics to characterize the
corresponding phase transitions. Our results clarify the effectiveness of SDP
relaxations in solving high-dimensional statistical problems.Comment: 71 pages, 24 pdf figure
When Social Influence Meets Item Inference
Research issues and data mining techniques for product recommendation and
viral marketing have been widely studied. Existing works on seed selection in
social networks do not take into account the effect of product recommendations
in e-commerce stores. In this paper, we investigate the seed selection problem
for viral marketing that considers both effects of social influence and item
inference (for product recommendation). We develop a new model, Social Item
Graph (SIG), that captures both effects in form of hyperedges. Accordingly, we
formulate a seed selection problem, called Social Item Maximization Problem
(SIMP), and prove the hardness of SIMP. We design an efficient algorithm with
performance guarantee, called Hyperedge-Aware Greedy (HAG), for SIMP and
develop a new index structure, called SIG-index, to accelerate the computation
of diffusion process in HAG. Moreover, to construct realistic SIG models for
SIMP, we develop a statistical inference based framework to learn the weights
of hyperedges from data. Finally, we perform a comprehensive evaluation on our
proposals with various baselines. Experimental result validates our ideas and
demonstrates the effectiveness and efficiency of the proposed model and
algorithms over baselines.Comment: 12 page
Automatic Bayesian Density Analysis
Making sense of a dataset in an automatic and unsupervised fashion is a
challenging problem in statistics and AI. Classical approaches for {exploratory
data analysis} are usually not flexible enough to deal with the uncertainty
inherent to real-world data: they are often restricted to fixed latent
interaction models and homogeneous likelihoods; they are sensitive to missing,
corrupt and anomalous data; moreover, their expressiveness generally comes at
the price of intractable inference. As a result, supervision from statisticians
is usually needed to find the right model for the data. However, since domain
experts are not necessarily also experts in statistics, we propose Automatic
Bayesian Density Analysis (ABDA) to make exploratory data analysis accessible
at large. Specifically, ABDA allows for automatic and efficient missing value
estimation, statistical data type and likelihood discovery, anomaly detection
and dependency structure mining, on top of providing accurate density
estimation. Extensive empirical evidence shows that ABDA is a suitable tool for
automatic exploratory analysis of mixed continuous and discrete tabular data.Comment: In proceedings of the Thirty-Third AAAI Conference on Artificial
Intelligence (AAAI-19
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
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