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 Statistical Learning


Margin Maximization as Lossless Maximal Compression

arXiv.org Machine Learning

The ultimate goal of a supervised learning algorithm is to produce models constructed on the training data that can generalize well to new examples. In classification, functional margin maximization -- correctly classifying as many training examples as possible with maximal confidence --has been known to construct models with good generalization guarantees. This work gives an information-theoretic interpretation of a margin maximizing model on a noiseless training dataset as one that achieves lossless maximal compression of said dataset -- i.e. extracts from the features all the useful information for predicting the label and no more. The connection offers new insights on generalization in supervised machine learning, showing margin maximization as a special case (that of classification) of a more general principle and explains the success and potential limitations of popular learning algorithms like gradient boosting. We support our observations with theoretical arguments and empirical evidence and identify interesting directions for future work.


Technical Background for "A Precision Medicine Approach to Develop and Internally Validate Optimal Exercise and Weight Loss Treatments for Overweight and Obese Adults with Knee Osteoarthritis"

arXiv.org Machine Learning

A precision medicine (PM) pipeline was developed to determine the optimal treatment regime for participants in an exercise (E), dietary weight loss (D), and D+E randomized clinical trial for knee osteoarthritis to maximize their expected outcomes. Using data from 343 participants of the Intensive Diet and Exercise for Arthritis (IDEA) trial, we applied 24 machine-learning models to develop individualized treatment rules on seven outcomes: SF-36 physical component score, weight loss, WOMAC pain/function/stiffness scores, compressive force, and IL-6. The optimal precision medicine model (PMM) was selected based on jackknife value function estimates that indicate improvement in the outcome(s) had future participants followed the estimated decision rule, which is then compared against the optimal single, fixed treatment model called zero-order model (ZOM) with a Z-test. Multiple outcome random forest was the optimal model for the WOMAC outcomes. The PMMs supported the overall findings from IDEA that the D+E intervention was optimal for most participants, but there was evidence that a subgroup of participants would likely benefit more from diet alone for two outcomes. This article provides detailed technical background for the clinical data analysis.


December 2019: "Top 40" New R Packages

#artificialintelligence

One hundred fifty-two packages made it to CRAN in December. Here are my "Top 40" picks in ten categories: Data, Genomics, Machine Learning, Mathematics, Medicine, Science, Statistics, Time Series, Utilities, and Visualization. Look here for more information as well as the vignette. Loads and creates spatial data, including layers and tools that are relevant to the activities of the Commission for the Conservation of Antarctic Marine Living Resources ( CCAMLR). Have a look at the vignette.


Survey of Network Intrusion Detection Methods from the Perspective of the Knowledge Discovery in Databases Process

arXiv.org Artificial Intelligence

The identification of cyberattacks which target information and communication systems has been a focus of the research community for years. Network intrusion detection is a complex problem which presents a diverse number of challenges. Many attacks currently remain undetected, while newer ones emerge due to the proliferation of connected devices and the evolution of communication technology. In this survey, we review the methods that have been applied to network data with the purpose of developing an intrusion detector, but contrary to previous reviews in the area, we analyze them from the perspective of the Knowledge Discovery in Databases (KDD) process. As such, we discuss the techniques used for the capture, preparation and transformation of the data, as well as, the data mining and evaluation methods. In addition, we also present the characteristics and motivations behind the use of each of these techniques and propose more adequate and up-to-date taxonomies and definitions for intrusion detectors based on the terminology used in the area of data mining and KDD. Special importance is given to the evaluation procedures followed to assess the different detectors, discussing their applicability in current real networks. Finally, as a result of this literature review, we investigate some open issues which will need to be considered for further research in the area of network security.


Improving Generalizability of Fake News Detection Methods using Propensity Score Matching

arXiv.org Machine Learning

Recently, due to the booming influence of online social networks, detecting fake news is drawing significant attention from both academic communities and general public. In this paper, we consider the existence of confounding variables in the features of fake news and use Propensity Score Matching (PSM) to select generalizable features in order to reduce the effects of the confounding variables. Experimental results show that the generalizability of fake news method is significantly better by using PSM than using raw frequency to select features. We investigate multiple types of fake news methods (classifiers) such as logistic regression, random forests, and support vector machines. We have consistent observations of performance improvement.


Masked cross self-attention encoding for deep speaker embedding

arXiv.org Machine Learning

In general, speaker verification tasks require the extraction of speaker embedding from a deep neural network. As speaker embedding may contain additional information such as noise besides speaker information, its variability controlling is needed. Our previous model have used multiple pooling based on shortcut connections to amplify speaker information by deepening the dimension; however, the problem of variability remains. In this paper, we propose a masked cross self-attention encoding (MCSAE) for deep speaker embedding. This method controls the variability of speaker embedding by focusing on each masked output of multiple pooling on each other. The output of the MCSAE is used to construct the deep speaker embedding. Experimental results on VoxCeleb data set demonstrate that the proposed approach improves performance as compared with previous state-of-the-art models.


On Newton Screening

arXiv.org Machine Learning

Screening and working set techniques are important approaches to reducing the size of an optimization problem. They have been widely used in accelerating first-order methods for solving large-scale sparse learning problems. In this paper, we develop a new screening method called Newton screening (NS) which is a generalized Newton method with a built-in screening mechanism. We derive an equivalent KKT system for the Lasso and utilize a generalized Newton method to solve the KKT equations. Based on this KKT system, a built-in working set with a relatively small size is first determined using the sum of primal and dual variables generated from the previous iteration, then the primal variable is updated by solving a least-squares problem on the working set and the dual variable updated based on a closed-form expression. Moreover, we consider a sequential version of Newton screening (SNS) with a warm-start strategy. We show that NS possesses an optimal convergence property in the sense that it achieves one-step local convergence. Under certain regularity conditions on the feature matrix, we show that SNS hits a solution with the same signs as the underlying true target and achieves a sharp estimation error bound with high probability. Simulation studies and real data analysis support our theoretical results and demonstrate that SNS is faster and more accurate than several state-of-the-art methods in our comparative studies.


Eigen-Stratified Models

arXiv.org Machine Learning

Stratified models depend in an arbitrary way on a selected categorical feature that takes $K$ values, and depend linearly on the other $n$ features. Laplacian regularization with respect to a graph on the feature values can greatly improve the performance of a stratified model, especially in the low-data regime. A significant issue with Laplacian-regularized stratified models is that the model is $K$ times the size of the base model, which can be quite large. We address this issue by formulating eigen-stratifed models, which are stratified models with an additional constraint that the model parameters are linear combinations of some modest number $m$ of bottom eigenvectors of the graph Laplacian, i.e., those associated with the $m$ smallest eigenvalues. With eigen-stratified models, we only need to store the $m$ bottom eigenvectors and the corresponding coefficients as the stratified model parameters. This leads to a reduction, sometimes large, of model size when $m \leq n$ and $m \ll K$. In some cases, the additional regularization implicit in eigen-stratified models can improve out-of-sample performance over standard Laplacian regularized stratified models.


COKE: Communication-Censored Kernel Learning for Decentralized Non-parametric Learning

arXiv.org Machine Learning

This paper studies the decentralized optimization and learning problem where multiple interconnected agents aim to learn an optimal decision function defined over a reproducing kernel Hilbert (RKH) space by jointly minimizing a global objective function, with access to locally observed data only. As a non-parametric approach, kernel learning faces a major challenge in distributed implementation: the decision variables of local objective functions are data-dependent with different sizes and thus cannot be optimized under the decentralized consensus framework without any raw data exchange among agents. To circumvent this major challenge and preserve data privacy, we leverage the random feature (RF) approximation approach to map the large-volume data represented in the RKH space into a smaller RF space, which facilitates the same-size parameter exchange and enables distributed agents to reach consensus on the function decided by the parameters in the RF space. For fast convergent implementation, we design an iterative algorithm for Decentralized Kernel Learning via Alternating direction method of multipliers (DKLA). Further, we develop a COmmunication-censored KErnel learning (COKE) algorithm to reduce the communication load in DKLA. To do so, we apply a communication-censoring strategy, which prevents an agent from transmitting at every iteration unless its local updates are deemed informative. Theoretical results in terms of linear convergence guarantee and generalization performance analysis of DKLA and COKE are provided. Comprehensive tests with both synthetic and real datasets are conducted to verify the communication efficiency and learning effectiveness of COKE.


Supervised Learning for Non-Sequential Data with the Canonical Polyadic Decomposition

arXiv.org Machine Learning

There has recently been increasing interest, both theoretical and practical, in utilizing tensor networks for the analysis and design of machine learning systems. In particular, a framework has been proposed that can handle both dense data (e.g., standard regression or classification tasks) and sparse data (e.g., recommender systems), unlike support vector machines and traditional deep learning techniques. Namely, it can be interpreted as applying local feature mappings to the data and, through the outer product operator, modelling all interactions of functions of the features; the corresponding weights are represented as a tensor network for computational tractability. In this paper, we derive efficient prediction and learning algorithms for supervised learning with the Canonical Polyadic (CP) decomposition, including suitable regularization and initialization schemes. We empirically demonstrate that the CP-based model performs at least on par with the existing models based on the Tensor Train (TT) decomposition on standard non-sequential tasks, and better on MovieLens 100K. Furthermore, in contrast to previous works which applied two-dimensional local feature maps to the data, we generalize the framework to handle arbitrarily high-dimensional maps, in order to gain a powerful lever on the expressiveness of the model. In order to enhance its stability and generalization capabilities, we propose a normalized version of the feature maps. Our experiments show that this version leads to dramatic improvements over the unnormalized and/or two-dimensional maps, as well as to performance on non-sequential supervised learning tasks that compares favourably with popular models, including neural networks.