Knowledge mining sensory evaluation data: genetic programming, statistical techniques, and swarm optimization

Knowledge mining sensory evaluation data is a challenging process due to extreme sparsity of the data, and a large variation in responses from different members (called assessors) of the panel. The main goals of knowledge mining in sensory sciences are understanding the dependency of the perceived liking score on the concentration levels of flavors’ ingredients, identifying ingredients that drive liking, segmenting the panel into groups with similar liking preferences and optimizing flavors to maximize liking per group. Our approach employs (1) Genetic programming (symbolic regression) and ensemble methods to generate multiple diverse explanations of assessor liking preferences with confidence information; (2) statistical techniques to extrapolate using the produced ensembles to unobserved regions of the flavor space, and segment the assessors into groups which either have the same propensity to like flavors, or are driven by the same ingredients; and (3) two-objective swarm optimization to identify flavors which are well and consistently liked by a selected segment of assessors

A Kernel Method for the Two-sample Problem

We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a third is based on the asymptotic distribution of this statistic. The test statistic can be computed in quadratic time, although efficient linear time approximations are available. Several classical metrics on distributions are recovered when the function space used to compute the difference in expectations is allowed to be more general (eg.~a Banach space). We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests

A Kernel Two-Sample Test

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD). We present two distribution-free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests

Kernel Methods for Classification with Irregularly Sampled and Contaminated Data.

Design of a classifier consists of two stages: feature extraction and classifier learning. For a better performance, the nature, characteristics, or underlying structure of data should be taken into account in either of the stages when we design a classifier. In this thesis, we present kernel methods for classification with irregularly sampled and contaminated data. First, we propose a feature extraction method for irregularly sampled data. Irregularly sampled data often arises in medical applications where the vital signs of patients are monitored based on the severity of their condition and the availability of nursing staff. In particular, we consider an ICU (intensive care unit) admission prediction problem for a post-operative patient with possible sepsis. The experimental results show that the proposed features, when paired with kernel methods, have more discriminating power than those used by clinicians. Second, we consider one-class classification problem with contaminated data, where the majority of the data comes from a "nominal" distribution with a small fraction of the data coming from an outlying distribution. We deal with this problem by robustly estimating the nominal density (or a level set thereof) from the contaminated data. Our proposed density estimation achieves robustness by combinining a traditional kernel density estimator (KDE) with ideas from classical M-estimation. The robustness of the density estimator is demonstrated with a representer theorem, the influence function, and experimental results. Third, we propose a kernel classifier that optimizes the L_2 distances between "difference of densities". Like a support vector machine (SVM), the classifier is sparse and results from solving a quadratic program. We also provide statistical performance guarantees for the proposed L_2 kernel classifier in the form of a finite sample oracle inequality, and strong consistency in the sense of both ISE and probability of error.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89858/1/stannum_1.pd

From Points to Probability Measures: Statistical Learning on Distributions with Kernel Mean Embedding

The dissertation presents a novel learning framework on probability measures which has abundant real-world applications. In classical setup, it is assumed that the data are points that have been drawn independent and identically (i.i.d.) from some unknown distribution. In many scenarios, however, representing data as distributions may be more preferable. For instance, when the measurement is noisy, we may tackle the uncertainty by treating the data themselves as distributions, which is often the case for microarray data and astronomical data where the measurement process is imprecise and replication is often required. Distributions not only embody individual data points, but also constitute information about their interactions which can be beneficial for structural learning in high-energy physics, cosmology, causality, and so on. Moreover, classical problems in statistics such as statistical estimation, hypothesis testing, and causal inference, may be interpreted in a decision-theoretic sense as machine learning problems on empirical distributions. Rephrasing these problems as such leads to novel approach for statistical inference and estimation. Hence, allowing learning algorithms to operate directly on distributions prompts a wide range of future applications. To work with distributions, the key methodology adopted in this thesis is the kernel mean embedding of distributions which represents each distribution as a mean function in a reproducing kernel Hilbert space (RKHS). In particular, the kernel mean embedding has been applied successfully in two-sample testing, graphical model, and probabilistic inference. On the other hand, this thesis will focus mainly on the predictive learning on distributions, i.e., when the observations are distributions and the goal is to make prediction about the previously unseen distributions. More importantly, the thesis investigates kernel mean estimation which is one of the most fundamental problems of kernel methods. Probability distributions, as opposed to data points, constitute information at a higher level such as aggregate behavior of data points, how the underlying process evolves over time and domains, and a complex concept that cannot be described merely by individual points. Intelligent organisms have the ability to recognize and exploit such information naturally. Thus, this work may shed light on future development of intelligent machines, and most importantly, may provide clues on the true meaning of intelligence

Graphical Models: Modeling, Optimization, and Hilbert Space Embedding

Over the past two decades graphical models have been widely used as a powerful tool for compactly representing distributions. On the other hand, kernel methods have also been used extensively to come up with rich representations. This thesis aims to combine graphical models with kernels to produce compact models with rich representational abilities. The following four areas are our focus. 1. Conditional random fields for multi-agent reinforcement learning. Conditional random fields (CRFs) are graphical models for modeling the probability of labels given the observations. They have traditionally assumed that, conditioned on the training data, the label sequences of different training examples are independent and identically distributed (iid). We extended the use of CRFs to a class of temporal learning algorithms, namely policy gradient reinforcement learning (RL). Now the labels are no longer iid. They are actions that update the environment and affect the next observation. From an RL point of view, CRFs provide a natural way to model joint actions in a decentralized Markov decision process. Using tree sampling for inference, our experiment shows the RL methods employing CRFs clearly outperform those which do not model the proper joint policy. 2. Bayesian online multi-label classification. Gaussian density filtering provides fast and effective inference for graphical models (Maybeck, 1982). Based on it, we propose a Bayesian online multi-label classification (BOMC) framework which learns a probabilistic model of the linear classifier. The training labels are incorporated to update the posterior of the classifiers via a graphical model similar to TrueSkill (Herbrich et al, 2007). Using samples from the posterior, we label the test data by maximizing the expected F1-score. In our experiments, BOMC delivers significantly higher macro-averaged F1-score than the state-of-the-art online maximum margin learners. 3. Hilbert space embedment of distributions. Graphical models are also an essential tool in kernel measures of independence for non-iid data. Traditional information theory often requires density estimation, which makes it unideal for statistical estimation. Motivated by the fact that distributions often appear in machine learning via expectations, we can characterize the distance between distributions in terms of distances between means, especially means in reproducing kernel Hilbert spaces which are called kernel embeddings. Under this framework, the undirected graphical models further allow us to factorize the kernel embeddings onto cliques, which yields efficient measures of independence for non-iid data (Zhang et al, 2009). 4. Optimization in maximum margin models for structured data. Maximum margin estimation for structured data is an important task where graphical models also play a key role. They are special cases of regularized risk minimization, for which bundle methods (BMRM, Teo et al, 2007) are a state-of-the-art general purpose solver. Smola et al (2007) proved that BMRM requires O(1/epsilon) iterations to converge to an epsilon accurate solution, and we further show that this rate hits the lower bound. Motivated by (Nesterov 2003, 2005), we utilized the composite structure of the objective function and devised an algorithm for the structured loss which converges to an epsilon accurate solution in O(1/sqrt{epsilon}) iterations

A Framework for Probability Density Estimation

The paper introduces a new framework for learning probability density functions. A theoretical analysis suggests that we can tailor a distribution for a class of tasks by training it to fit a small subsample. Experimental evidence is given to support the theoretical analysis