Optimization algorithms for inference and classification of genetic profiles from undersampled measurements

In this thesis, we tackle three different problems, all related to optimization techniques for inference and classification of genetic profiles. First, we extend the deterministic Non-negative Matrix Factorization (NMF) framework to the probabilistic case (PNMF). We apply the PNMF algorithm to cluster and classify DNA microarrays data. The proposed PNMF is shown to outperform the deterministic NMF and the sparse NMF algorithms in clustering stability and classification accuracy. Second, we propose SMURC: Small-sample MUltivariate Regression with Covariance estimation. Specifically, we consider a high dimension low sample-size multivariate regression problem that accounts for correlation of the response variables. We show that, in this case, the maximum likelihood approach is senseless because the likelihood diverges. We propose a normalization of the likelihood function that guarantees convergence. Simulation results show that SMURC outperforms the regularized likelihood estimator with known covariance matrix and the state-of-the-art sparse Conditional Graphical Gaussian Model (sCGGM). In the third Chapter, we derive a new greedy algorithm that provides an exact sparse solution of the combinatorial l sub zero-optimization problem in an exponentially less computation time. Unlike other greedy approaches, which are only approximations of the exact sparse solution, the proposed greedy approach, called Kernel reconstruction, leads to the exact optimal solution

Preference Modeling in Data-Driven Product Design: Application in Visual Aesthetics

Creating a form that is attractive to the intended market audience is one of the greatest challenges in product development given the subjective nature of preference and heterogeneous market segments with potentially different product preferences. Accordingly, product designers use a variety of qualitative and quantitative research tools to assess product preferences across market segments, such as design theme clinics, focus groups, customer surveys, and design reviews; however, these tools are still limited due to their dependence on subjective judgment, and being time and resource intensive. In this dissertation, we focus on a key research question: how can we understand and predict more reliably the preference for a future product in heterogeneous markets, so that this understanding can inform designers' decision-making? We present a number of data-driven approaches to model product preference. Instead of depending on any subjective judgment from human, the proposed preference models investigate the mathematical patterns behind users’ choice and behavior. This allows a more objective translation of customers' perception and preference into analytical relations that can inform design decision-making. Moreover, these models are scalable in that they have the capacity to analyze large-scale data and model customer heterogeneity accurately across market segments. In particular, we use feature representation as an intermediate step in our preference model, so that we can not only increase the predictive accuracy of the model but also capture in-depth insight into customers' preference. We tested our data-driven approaches with applications in visual aesthetics preference. Our results show that the proposed approaches can obtain an objective measurement of aesthetic perception and preference for a given market segment. This measurement enables designers to reliably evaluate and predict the aesthetic appeal of their designs. We also quantify the relative importance of aesthetic attributes when both aesthetic attributes and functional attributes are considered by customers. This quantification has great utility in helping product designers and executives in design reviews and selection of designs. Moreover, we visualize the possible factors affecting customers' perception of product aesthetics and how these factors differ across different market segments. Those visualizations are incredibly important to designers as they relate physical design details to psychological customer reactions. The main contribution of this dissertation is to present purely data-driven approaches that enable designers to quantify and interpret more reliably the product preference. Methodological contributions include using modern probabilistic approaches and feature learning algorithms to quantitatively model the design process involving product aesthetics. These novel approaches can not only increase the predictive accuracy but also capture insights to inform design decision-making.PHDDesign ScienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145987/1/yanxinp_1.pd

Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, sometimes even better than, the original dense networks. Sparsity promises to reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

l0 Sparse signal processing and model selection with applications

Sparse signal processing has far-reaching applications including compressed sensing, media compression/denoising/deblurring, microarray analysis and medical imaging. The main reason for its popularity is that many signals have a sparse representation given that the basis is suitably selected. However the difficulty lies in developing an efficient method of recovering such a representation. To this aim, two efficient sparse signal recovery algorithms are developed in the first part of this thesis. The first method is based on direct minimization of the l0 norm via cyclic descent, which is called the L0LS-CD (l0 penalized least squares via cyclic descent) algorithm. The other method minimizes smooth approximations of sparsity measures including those of the l0 norm via the majorization minimization (MM) technique, which is called the QC (quadratic concave) algorithm. The L0LS-CD algorithm is developed further by extending it to its multivariate (V-L0LS-CD (vector L0LS-CD)) and group (gL0LS-CD (group L0LS-CD)) regression variants. Computational speed-ups to the basic cyclic descent algorithm are discussed and a greedy version of L0LS-CD is developed. Stability of these algorithms is analyzed and the impact of the penalty parameter and proper initialization on the algorithm performance are highlighted. A suitable method for performance comparison of sparse approximating algorithms in the presence of noise is established. Simulations compare L0LS-CD and V-L0LS-CD with a range of alternatives on under-determined as well as over-determined systems. The QC algorithm is applicable to a class of penalties that are neither convex nor concave but have what we call the quadratic concave property. Convergence proofs of this algorithm are presented and it is compared with the Newton algorithm, concave convex (CC) procedure, as well as with the class of proximity algorithms. Simulations focus on the smooth approximations of the l0 norm and compare them with other l0 denoising algorithms. Next, two applications of sparse modeling are considered. In the first application the L0LS-CD algorithm is extended to recover a sparse transfer function in the presence of coloured noise. The second uses gL0LS-CD to recover the topology of a sparsely connected network of dynamic systems. Both applications use Laguerre basis functions for model expansion. The role of model selection in sparse signal processing is widely neglected in literature. The tuning/penalty parameter of a sparse approximating problem should be selected using a model selection criterion which minimizes a desired discrepancy measure. Compared to the commonly used model selection methods, the SURE (Stein's unbiased risk estimator) estimator stands out as one which does not suffer from the limitations of other methods. Most model selection criterion are developed based on signal or prediction mean squared error. The last section of this thesis develops an SURE criterion instead for parameter mean square error and applies this result to l1 penalized least squares problem with grouped variables. Simulations based on topology identification of a sparse network are presented to illustrate and compare with alternative model selection criteria