arXiv subjects

Jamie Haddock

Publications and source records attributed to Jamie Haddock.

31 records · Page 2Linked to original sources

arXiv2021

Statistical Learning for Best Practices in Tattoo Removal

The causes behind complications in laser-assisted tattoo removal are currently not well understood, and in the literature relating to tattoo removal the emphasis on removal treatment is on removal technologies and tools, not best parameters involved in the treatment process. Additionally, the very challenge of determining best practices is difficult given the complexity of interactions between factors that may correlate to these complications. In this paper we apply a battery of classical statistical methods and techniques to identify features that may be closely correlated to causes of complication during the tattoo removal process, and report quantitative evidence for potential best practices. We develop elementary statistical descriptions of tattoo data collected by the largest gang rehabilitation and reentry organization in the world, Homeboy Industries; perform parametric and nonparametric tests of significance; and finally, produce a statistical model explaining treatment parameter interactions, as well as develop a ranking system for treatment parameters utilizing bootstrapping and gradient boosting.

stat.AP↗

arXiv2021

On a Guided Nonnegative Matrix Factorization

Fully unsupervised topic models have found fantastic success in document clustering and classification. However, these models often suffer from the tendency to learn less-than-meaningful or even redundant topics when the data is biased towards a set of features. For this reason, we propose an approach based upon the nonnegative matrix factorization (NMF) model, deemed \textit{Guided NMF}, that incorporates user-designed seed word supervision. Our experimental results demonstrate the promise of this model and illustrate that it is competitive with other methods of this ilk with only very little supervision information.

cs.LG↗

arXiv2020

On Application of Block Kaczmarz Methods in Matrix Factorization

Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this task utilize an exact least-squares solver whose computation is time consuming and memory-expensive. In this paper we discuss and test a block Kaczmarz solver that replaces the least-squares subroutine in the common alternating scheme for matrix factorization. This variant trades a small increase in factorization error for significantly faster algorithmic performance. In doing so we find block sizes that produce a solution comparable to that of the least-squares solver for only a fraction of the runtime and working memory requirement.

math.NA↗

arXiv2020

On Large-Scale Dynamic Topic Modeling with Nonnegative CP Tensor Decomposition

There is currently an unprecedented demand for large-scale temporal data analysis due to the explosive growth of data. Dynamic topic modeling has been widely used in social and data sciences with the goal of learning latent topics that emerge, evolve, and fade over time. Previous work on dynamic topic modeling primarily employ the method of nonnegative matrix factorization (NMF), where slices of the data tensor are each factorized into the product of lower-dimensional nonnegative matrices. With this approach, however, information contained in the temporal dimension of the data is often neglected or underutilized. To overcome this issue, we propose instead adopting the method of nonnegative CANDECOMP/PARAPAC (CP) tensor decomposition (NNCPD), where the data tensor is directly decomposed into a minimal sum of outer products of nonnegative vectors, thereby preserving the temporal information. The viability of NNCPD is demonstrated through application to both synthetic and real data, where significantly improved results are obtained compared to those of typical NMF-based methods. The advantages of NNCPD over such approaches are studied and discussed. To the best of our knowledge, this is the first time that NNCPD has been utilized for the purpose of dynamic topic modeling, and our findings will be transformative for both applications and further developments.

cs.LG↗

arXiv2020

Semi-supervised NMF Models for Topic Modeling in Learning Tasks

We propose several new models for semi-supervised nonnegative matrix factorization (SSNMF) and provide motivation for SSNMF models as maximum likelihood estimators given specific distributions of uncertainty. We present multiplicative updates training methods for each new model, and demonstrate the application of these models to classification, although they are flexible to other supervised learning tasks. We illustrate the promise of these models and training methods on both synthetic and real data, and achieve high classification accuracy on the 20 Newsgroups dataset.

cs.LG↗

arXiv2020

Feature Selection on Lyme Disease Patient Survey Data

Lyme disease is a rapidly growing illness that remains poorly understood within the medical community. Critical questions about when and why patients respond to treatment or stay ill, what kinds of treatments are effective, and even how to properly diagnose the disease remain largely unanswered. We investigate these questions by applying machine learning techniques to a large scale Lyme disease patient registry, MyLymeData, developed by the nonprofit LymeDisease.org. We apply various machine learning methods in order to measure the effect of individual features in predicting participants' answers to the Global Rating of Change (GROC) survey questions that assess the self-reported degree to which their condition improved, worsened, or remained unchanged following antibiotic treatment. We use basic linear regression, support vector machines, neural networks, entropy-based decision tree models, and $k$-nearest neighbors approaches. We first analyze the general performance of the model and then identify the most important features for predicting participant answers to GROC. After we identify the "key" features, we separate them from the dataset and demonstrate the effectiveness of these features at identifying GROC. In doing so, we highlight possible directions for future study both mathematically and clinically.

cs.CY↗

arXiv2020

Greed Works: An Improved Analysis of Sampling Kaczmarz-Motzkin

Stochastic iterative algorithms have gained recent interest in machine learning and signal processing for solving large-scale systems of equations, $Ax=b$. One such example is the Randomized Kaczmarz (RK) algorithm, which acts only on single rows of the matrix $A$ at a time. While RK randomly selects a row of $A$ to work with, Motzkin's Method (MM) employs a greedy row selection. Connections between the two algorithms resulted in the Sampling Kaczmarz-Motzkin (SKM) algorithm which samples a random subset of $β$ rows of $A$ and then greedily selects the best row of the subset. Despite their variable computational costs, all three algorithms have been proven to have the same theoretical upper bound on the convergence rate. In this work, an improved analysis of the range of random (RK) to greedy (MM) methods is presented. This analysis improves upon previous known convergence bounds for SKM, capturing the benefit of partially greedy selection schemes. This work also further generalizes previous known results, removing the theoretical assumptions that $β$ must be fixed at every iteration and that $A$ must have normalized rows.

math.NA↗

arXiv2019

Data-driven Algorithm Selection and Parameter Tuning: Two Case studies in Optimization and Signal Processing

Machine learning algorithms typically rely on optimization subroutines and are well-known to provide very effective outcomes for many types of problems. Here, we flip the reliance and ask the reverse question: can machine learning algorithms lead to more effective outcomes for optimization problems? Our goal is to train machine learning methods to automatically improve the performance of optimization and signal processing algorithms. As a proof of concept, we use our approach to improve two popular data processing subroutines in data science: stochastic gradient descent and greedy methods in compressed sensing. We provide experimental results that demonstrate the answer is ``yes'', machine learning algorithms do lead to more effective outcomes for optimization problems, and show the future potential for this research direction.

cs.LG↗

arXiv2019

On Inferences from Completed Data

Matrix completion has become an extremely important technique as data scientists are routinely faced with large, incomplete datasets on which they wish to perform statistical inferences. We investigate how error introduced via matrix completion affects statistical inference. Furthermore, we prove recovery error bounds which depend upon the matrix recovery error for several common statistical inferences. We consider matrix recovery via nuclear norm minimization and a variant, $\ell_1$-regularized nuclear norm minimization for data with a structured sampling pattern. Finally, we run a series of numerical experiments on synthetic data and real patient surveys from MyLymeData, which illustrate the relationship between inference recovery error and matrix recovery error. These results indicate that exact matrix recovery is often not necessary to achieve small inference recovery error.

math.ST↗

arXiv2019

A Sampling Kaczmarz-Motzkin Algorithm for Linear Feasibility

We combine two iterative algorithms for solving large-scale systems of linear inequalities, the relaxation method of Agmon, Motzkin et al. and the randomized Kaczmarz method. In doing so, we obtain a family of algorithms that generalize and extend both techniques. We prove several convergence results, and our computational experiments show our algorithms often outperform the original methods.

math.OC↗

arXiv2018

Randomized Projection Methods for Linear Systems with Arbitrarily Large Sparse Corruptions

In applications like medical imaging, error correction, and sensor networks, one needs to solve large-scale linear systems that may be corrupted by a small number of arbitrarily large corruptions. We consider solving such large-scale systems of linear equations $A\mathbf{x}=\mathbf{b}$ that are inconsistent due to corruptions in the measurement vector $\mathbf{b}$. With this as our motivating example, we develop an approach for this setting that allows detection of the corrupted entries and thus convergence to the "true" solution of the original system. We provide analytical justification for our approaches as well as experimental evidence on real and synthetic systems.

math.NA↗

arXiv2018

On Motzkin's Method for Inconsistent Linear Systems

Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. The relaxation method, or Motzkin's method, can be viewed as an iterative method that projects the current estimation onto the solution hyperplane corresponding to the most violated constraint. Although this leads to an optimal selection strategy for consistent systems, for inconsistent least square problems, the strategy presents a tradeoff between convergence rate and solution accuracy. We provide a theoretical analysis that shows Motzkin's method offers an initially accelerated convergence rate and this acceleration depends on the dynamic range of the residual. We quantify this acceleration for Gaussian systems as a concrete example. Lastly, we include experimental evidence on real and synthetic systems that support the analysis.

math.NA↗

arXiv2017

The Minimum Euclidean-Norm Point on a Convex Polytope: Wolfe's Combinatorial Algorithm is Exponential

The complexity of Philip Wolfe's method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. The method is important because it is used as a subroutine for one of the most practical algorithms for submodular function minimization. We present the first example that Wolfe's method takes exponential time. Additionally, we improve previous results to show that linear programming reduces in strongly-polynomial time to the minimum norm point problem over a simplex.

math.OC↗