Applied Math Seminar

Sparse Additive Modeling

10/30/2017 - 4:15pm
10/30/2017 - 5:15pm
Speaker: 
Prof. Noah Simon (Department of Biostatistics, University of Washington)
Abstract: 

With recent advances in high-throughput technology it is now common to collect enormous quantities of data on a small number of subjects. In particular, in the biomedical field, we often collect extremely high dimensional biomolecular information (eg. gene expression, dna-sequence, and/or epigenetic information). We are often interested in using this information to predict a phenotype: eg. does a person have a given disease? Or is a tumor susceptible to a particular therapy? In these cases we often believe that only a small subset of the biomolecular features are informative for the phenotypic response (though we generally do not know which). Given this, we would like a model-building procedure that selects and uses only a small subset of the available genomic features for predicting phenotype.

The LASSO is one common method that both performs feature selection, and fits a linear model on that selected subset. The LASSO is an attractive method as it is simple, has good theoretical behaviour, is computationally straightforward to fit, and empirically performs well in many applications. However, a linear model may sometimes not be a good approximation to the true underlying relationship between features and response. In this presentation we will discuss Sparse Additive Modeling, an extension to the LASSO that selects features, and fits a more flexible additive model in those features. This, more flexible framework, shares many of the attractive properties of the LASSO (parsimony, computational tractibility, theoretical guarantees, and empirical performance). In addition, in non-linear scenarios it may more adequately model our data.

(hopefully) Very little background will be assumed in this talk: We will begin by introducing and discussing the LASSO, non-parametric regression, and additive modeling. In addition, we will touch on convex optimization and numerical algorithms for high dimensional minimization.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

TBA

12/04/2017 - 4:15pm
12/04/2017 - 5:15pm
Speaker: 
Prof. Lyuba Kuznetsova (SDSU)
Abstract: 

 TBA

Where: 
Mondays 4:15-5:15 pm Emmy Noether Rm Millikan 1021 Pomona College

Machine Learning in the Web World

09/21/2017 - 4:15pm
09/21/2017 - 5:15pm
Speaker: 
Alpan Raval (CGU, Keck Graduate Institute)
Abstract: 

In this talk I will present a very high-level (equation-free) overview of some Machine Learning (ML) projects at LinkedIn and the data used to drive them. I will describe the problems and discuss the challenges in implementing ML solutions to these problems. Many of these challenges are common to large internet companies — examples include: high volumes of dynamic data, noisy ground truth, and time-to-inference requirements — while a few are specific to the LinkedIn platform.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

TBA

11/27/2017 - 5:30pm
11/27/2017 - 6:30pm
Speaker: 
Sergey Vladimir Lototsky (USC)
Abstract: 

 TBA

Where: 
Emmy Noether Rm, Millikan 1021, Pomona

Numerical Methods for Reaction-Diffusion Equations and the Application in Computational Biology

10/23/2017 - 4:15pm
10/23/2017 - 5:15pm
Speaker: 
Weitao Chen (UCR)
Abstract: 

Reaction-diffusion equations have wide applications in natural and engineering sciences. The efficiency of numerical methods for these equations is often limited by the severe stability conditions due to diffusion and stiff reactions, as well as the curse of dimensionality for equations in high-dimensional spaces. We developed a numerical method to improve the efficiency by relaxing stability constraints, coupled with sparse grid technique, for solving reaction-diffusion equations in high dimensions. We also extend this method to more general systems with nonhomogeneous boundary conditions or explicitly time-dependent reactions. In addition, I will introduce its application in modeling a complex biological system, the macropatterning in mouse tongue, to understand the robustness strategies in pattern formation on a growing tissue.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

Streaming t-SNE

10/09/2017 - 4:15pm
10/09/2017 - 5:15pm
Speaker: 
Mariam Salloum (CMC)
Abstract: 

Data sets involving many dimensions are commonplace in scientific computing and machine learning, however, the human visual system is limited to interpreting data in only two or three dimensions. An award-wining technique called Student-T Stochastic Neighbor Embedding (t-SNE) has been presented to embed data of high dimension into a 2-D or 3-D space, while preserving local relationships in the original data. This has yielded marked improvements in the quality of the embedding, especially with regard to its ability to preserve clustering and structure. However, the original t-SNE can only be used in batch mode, i.e. all data must be available prior to the start of the algorithm. It is therefore compelling to have a version of t-SNE which can accommodate a streaming operational mode, i.e. to incorporate new information into the embedded representation as it arrives. Such a system would allow an operator to observe changes in complex, high dimensional data in near real-time. In this work, we present a streaming t-SNE variation and provide visualizations with streaming data.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

organizational discussion

09/04/2017 - 4:15pm
09/04/2017 - 5:15pm
Speaker: 
TBA
Abstract: 

 TBA

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

TBA

11/13/2017 - 4:15pm
11/13/2017 - 5:15pm
Speaker: 
Cecile Piret (Michigan Tech University)
Abstract: 

 TBA

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

RNA Interactions - a PDE Story

09/18/2017 - 4:15pm
09/18/2017 - 5:15pm
Speaker: 
Maryann Hohn (UCSD)
Abstract: 

Small non-coding RNAs regulate developmental events through certain interactions with messenger RNA (mRNA). By binding to specific sites on a strand of mRNA, small RNAs may cause a gene to be activated or suppressed, turning a gene "on" or "off". To better understand these interactions, we developed a mathematical model that consists of a system of coupled partial differential equations describing mRNA and small RNA interactions across cells and tissue. In this talk, we will discuss the mathematical models created and numerical simulations using these equations.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

Reduced Order Models of Fractured Systems using Graph Theory and Machine Learning

05/09/2017 - 11:00am
05/09/2017 - 12:00pm
Speaker: 
Gowri Srinivasan (LANL)
Abstract: 

Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for two timely applications of interest to LANL: dynamic fracture processes like spall and fragmentation in metals (weapons performance) and detection of gas flow in static fractures in rock due to underground explosions (nuclear nonproliferation). Micro-fracture information is only known in a statistical sense, so representing millions of micro-fractures in 1000s of model runs to bound the uncertainty requires petabytes of information. Our critical advance is to integrate computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive grid-based models to efficient graphs with at least 3 orders of magnitude speedup for Discrete Fracture Networks (DFNs).

Where: 
CGU Math South
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