Statistics and Probability Seminars

ISL & Stats present Stability and uncertainty quantification

Topic: 
Bridging convex and nonconvex optimization in noisy matrix completion: Stability and uncertainty quantification
Abstract / Description: 

This talk is concerned with noisy matrix completion: given partial and corrupted entries of a large low-rank matrix, how to estimate and infer the underlying matrix? Arguably one of the most popular paradigms to tackle this problem is convex relaxation, which achieves remarkable efficacy in practice. However, the statistical stability guarantees of this approach is still far from optimal in the noisy setting, falling short of explaining the empirical success. Moreover, it is generally very challenging to pin down the distributions of the convex solution, which presents a major roadblock in assessing the uncertainty, or "confidence", for the obtained estimates–a crucial task at the core of statistical inference. 

Our recent work makes progress towards understanding stability and uncertainty quantification for noisy matrix completion. When the rank of the unknown matrix is a constant: (1) we demonstrate that convex programming achieves near-optimal estimation errors vis-'avis random noise; (2) we develop a de-biased estimator that admits accurate distributional characterizations, thus enabling asymptotically optimal inference. All of this is enabled by bridging convex relaxation with the nonconvex approach, a seemingly distinct algorithmic paradigm that is provably robust against noise.


This is joint work with Cong Ma, Yuling Yan, Yuejie Chi, and Jianqing Fan.

Date and Time: 
Tuesday, May 28, 2019 - 4:30pm
Venue: 
Herrin Hall Room T175

#StanfordToo: A Conversation about Sexual Harassment in Our Academic Spaces

Topic: 
#StanfordToo: A Conversation about Sexual Harassment in Our Academic Spaces
Abstract / Description: 

Individuals of all genders invited to be a part of:
#StanfordToo: A Conversation about Sexual Harassment in Our Academic Spaces, where we will feature real stories of harassment at Stanford academic STEM in a conversation with Provost Drell, Dean Minor (SoM), and Dean Graham (SE3). We will have plenty of time for audience discussion on how we can take concrete action to dismantle this culture and actively work towards a more inclusive Stanford for everyone. While our emphasis is on STEM fields, we welcome and encourage participation from students, postdocs, staff, and faculty of all academic disciplines and backgrounds.

Date and Time: 
Friday, April 19, 2019 - 3:30pm
Venue: 
STLC 111

OSA/SPIE, SPRC and Ginzton Lab present "Frequency comb-based nonlinear spectroscopy"

Topic: 
Frequency comb-based nonlinear spectroscopy
Abstract / Description: 

Rapid and precise measurements are and always have been of interest in science and technology partly because of their numerous practical applications. Since their development, frequency comb-based methods have revolutionized optical measurements. They simultaneously provide high resolution, high sensitivity, and rapid acquisition times. These methods are being developed for use in many fields, from atomic and molecular spectroscopy, to precision metrology, to spectral LIDAR and even atmospheric monitoring. However they cannot address the issues of inhomogeneously broadened transitions or sample heterogeneity. This is especially important for remote chemical sensing applications.

In this talk I will discuss a novel optical method, that I recently developed, which overcomes these limitations. I will demonstrate its capabilities for probing extremely weak fundamental processes as well as its applications for rapid and high resolution chemical sensing.

 

References:

B. Lomsadze, B. Smith and S. T. Cundiff. "Tri-comb spectroscopy". Nature Photonics 12, 676, 2018.
B. Lomsadze and S. T. Cundiff. "Frequency-comb based double-quantum two-dimensional spectrum identifies collective hyperfine resonances in atomic vapor induced by dipole-dipole interactions." Physical Review Letters 120, 233401, 2018.
B. Lomsadze and S. T. Cundiff. "Frequency combs enable rapid and high-resolution multidimensional coherent spectroscopy". Science 357, 1389, 2017
B. Lomsadze and S. T. Cundiff. "Frequency comb-based four-wave-mixing spectroscopy". Optics letters 42, 2346, 2017

Date and Time: 
Wednesday, June 12, 2019 - 4:15pm
Venue: 
Allen 101X

RESCHEDULED: OSA/SPIE, SPRC and Ginzton Lab present "Frequency comb-based nonlinear spectroscopy"

Topic: 
RESCHEDULED: Frequency comb-based nonlinear spectroscopy: Bridging the gap between fundamental science and cutting-edge technology
Abstract / Description: 

RESCHEDULED for June 12

Rapid and precise measurements are and always have been of interest in science and technology partly because of their numerous practical applications. Since their development, frequency comb-based methods have revolutionized optical measurements. They simultaneously provide high resolution, high sensitivity, and rapid acquisition times. These methods are being developed for use in many fields, from atomic and molecular spectroscopy, to precision metrology, to spectral LIDAR and even atmospheric monitoring. However they cannot address the issues of inhomogeneously broadened transitions or sample heterogeneity. This is especially important for remote chemical sensing applications.

In this talk I will discuss a novel optical method, that I recently developed, which overcomes these limitations. I will demonstrate its capabilities for probing extremely weak fundamental processes as well as its applications for rapid and high resolution chemical sensing.

 

References:

B. Lomsadze, B. Smith and S. T. Cundiff. "Tri-comb spectroscopy". Nature Photonics 12, 676, 2018.
B. Lomsadze and S. T. Cundiff. "Frequency-comb based double-quantum two-dimensional spectrum identifies collective hyperfine resonances in atomic vapor induced by dipole-dipole interactions." Physical Review Letters 120, 233401, 2018.
B. Lomsadze and S. T. Cundiff. "Frequency combs enable rapid and high-resolution multidimensional coherent spectroscopy". Science 357, 1389, 2017
B. Lomsadze and S. T. Cundiff. "Frequency comb-based four-wave-mixing spectroscopy". Optics letters 42, 2346, 2017

Date and Time: 
Wednesday, March 20, 2019 - 4:15pm
Venue: 
Allen 101X

John G. Linvill Distinguished Seminar on Electronic Systems Technology

Topic: 
Internet of Things and Internet of Energy for Connecting at Any Time and Any Place
Abstract / Description: 

In this presentation, I would like to discuss with you how to establish a sustainable and smart society through the internet of energy for connecting at any time and any place. I suspect that you have heard the phrase, "Internet of Energy" less often. The meaning of this phrase is simple. Because of a ubiquitous energy transmission system, you do not need to worry about a shortage of electric power. One of the most important items for establishing a sustainable society is [...]


"Inaugural Linvill Distinguished Seminar on Electronic Systems Technology," EE News, July 2018

 

Date and Time: 
Monday, January 14, 2019 - 4:30pm
Venue: 
Hewlett 200

Statistics Seminar: Inference, Computation, and Visualization for Convex Clustering and Biclustering

Topic: 
Inference, Computation, and Visualization for Convex Clustering and Biclustering
Abstract / Description: 

Hierarchical clustering enjoys wide popularity because of its fast computation, ease of interpretation, and appealing visualizations via the dendogram and cluster heatmap. Recently, several have proposed and studied convex clustering and biclustering which, similar in spirit to hierarchical clustering, achieve cluster merges via convex fusion penalties. While these techniques enjoy superior statistical performance, they suffer from slower computation and are not generally conducive to representation as a dendogram. In the first part of the talk, we present new convex (bi)clustering methods and fast algorithms that inherit all of the advantages of hierarchical clustering. Specifically, we develop a new fast approximation and variation of the convex (bi)clustering solution path that can be represented as a dendogram or cluster heatmap. Also, as one tuning parameter indexes the sequence of convex (bi)clustering solutions, we can use these to develop interactive and dynamic visualization strategies that allow one to watch data form groups as the tuning parameter varies. In the second part of this talk, we consider how to conduct inference for convex clustering solutions that addresses questions like: Are there clusters in my data set? Or, should two clusters be merged into one? To achieve this, we develop a new geometric representation of Hotelling's T2-test that allows us to use the selective inference paradigm to test multivariate hypotheses for the first time. We can use this approach to test hypotheses and calculate confidence ellipsoids on the cluster means resulting from convex clustering. We apply these techniques to examples from text mining and cancer genomics.

This is joint work with John Nagorski and Frederick Campbell.


The Statistics Seminars for Winter Quarter will be held in Room 380Y of the Sloan Mathematics Center in the Main Quad at 4:30pm on Tuesdays. 

Date and Time: 
Tuesday, March 13, 2018 - 4:30pm
Venue: 
Sloan Mathematics Building, Room 380Y

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