Statistics and Probability Seminars

Statistics Department Seminar presents "The relevance problem: 50 years on"

Topic: 
"The relevance problem: 50 years on"
Abstract / Description: 

Given a large cohort of "similar" cases Z1, . . . , ZN one can construct an efficient statistical inference procedure by 'learning from the experience of others' (also known as "borrowing strength" from the ensemble). But what if, instead, we observe a massive database where each case is accompanied with extra contextual information (usually in the form of covariates), making the Zi's non-exchangeable? It's not obvious how we go about gathering strength when each piece of information is fuzzy and heterogeneous. Moreover, if we include irrelevant cases, borrowing information can heavily damage the quality of the inference! This raises some fundamental questions: when (not) to borrow? whom (not) to borrow? how (not) to borrow? These questions are at the heart of the "Problem of Relevance" in statistical inference – a puzzle that remained too little addressed since its inception nearly half a century ago (Efron and Morris, 1971,1972; Efron 2019). The purpose of this talk is to present an attempt to develop basic principles and practical guidelines in order to tackle some of the unsettled issues that surround the relevance problem. Through examples, we will demonstrate how our new statistical perspective answers previously unanswerable questions in a realistic and feasible way.


This is a joint work with my previous student Kaijun Wang, who is currently a postdoctoral research fellow at Fred Hutchinson Cancer Research Center.

Date and Time: 
Thursday, July 25, 2019 - 4:30pm
Venue: 
Sequoia Hall Room 200

Statistics Department Seminar presents "Augmented minimax linear estimation"

Topic: 
Augmented minimax linear estimation
Abstract / Description: 

Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized treatments. In this talk, we discuss a general approach to estimating such quantities: we begin with a simple plug-in estimator based on an estimate of the conditional expectation function, and then correct the plug-in estimator by subtracting a minimax linear estimate of its error. We show that our method is semiparametrically efficient under weak conditions and observe promising performance on both real and simulated data.

Date and Time: 
Tuesday, August 6, 2019 - 4:30pm
Venue: 
Sloan Mathematics Center, Room 380C

Statistics Department Seminar presents "Analytical nonlinear shrinkage of large-dimensional covariance matrices"

Topic: 
Analytical nonlinear shrinkage of large-dimensional covariance matrices
Abstract / Description: 

This paper establishes the first analytical formula for optimal nonlinear shrinkage of largedimensional covariance matrices. We achieve this by identifying and mathematically exploiting a deep connection between nonlinear shrinkage and nonparametric estimation of the Hilbert transform of the sample spectral density. Previous nonlinear shrinkage methods were numerical: QuEST requires numerical inversion of a complex equation from random matrix theory whereas NERCOME is based on a sample-splitting scheme. The new analytical approach is more elegant and also has more potential to accommodate future variations or extensions. Immediate benefits are that it is typically 1,000 times faster with the same accuracy and accommodates covariance matrices of dimension up to 10,000. The difficult case where the matrix dimension exceeds the sample size is also covered.

Date and Time: 
Tuesday, July 30, 2019 - 4:30pm
Venue: 
Sloan Mathematics Center, Room 380C

Statistics Department Seminar presents "A geometric perspective on false discovery control"

Topic: 
A geometric perspective on false discovery control
Abstract / Description: 

A common approach to statistical model selection — particularly in scientific domains in which it is of interest to draw inferences about an underlying phenomenon — is to develop powerful procedures that provide control on false discoveries. Such methods are widely used in inferential settings involving variable selection, graph estimation, and others in which a discovery is naturally regarded as a discrete concept. However, this view of a discovery is ill-suited to many model selection and structured estimation problems in which the underlying decision space is not discrete. We describe a geometric reformulation of the notion of a discovery, which enables the development of model selection methodology for a broader class of problems. We highlight the utility of this viewpoint in problems involving subspace selection and low-rank estimation, with a specific algorithm to control for false discoveries in these settings.

 


This is joint work with Parikshit Shah and Venkat Chandrasekaran.

Date and Time: 
Tuesday, July 23, 2019 - 4:30pm
Venue: 
Sloan Mathematics Center, Room 380C

Statistics Department Seminar presents "Reproducible localization of causal variants across the genome"

Topic: 
Reproducible localization of causal variants across the genome
Abstract / Description: 

We present a powerful and flexible statistical method for the genetic mapping of complex traits. This method, which we call KnockoffZoom, provably controls the false discovery rate using knockoff genotypes as negative controls, while trying to localize causal variants as precisely as possible. Our inferences are equally valid for quantitative and binary phenotypes, making no assumptions about their genetic architectures. Instead, we leverage well-established genetic models to account for linkage disequilibrium and population structure. We demonstrate that this method detects more associations than mixed effects models and achieves fine-mapping precision, at comparable computational cost. Lastly, we apply KnockoffZoom to data from the UK Biobank and report many new findings.

Date and Time: 
Tuesday, July 16, 2019 - 4:30pm
Venue: 
Sloan Mathematics Center, Room 380C

Statistics Department Seminar presents "Metropolized knockoff sampling"

Topic: 
Metropolized knockoff sampling
Abstract / Description: 

Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which can discover true effects while rigorously controlling the expected fraction of false positives. A remaining challenge to apply this method is to construct knockoff variables, which are synthetic variables obeying a crucial exchangeability property with the explanatory variables under study. This paper introduces techniques for knockoff generation in great generality: we provide a sequential characterization of all possible knockoff distributions, which leads to a Metropolis-Hastings formulation of an exact knockoff sampler. We further show how to use conditional independence structure to speed up computations. Combining these two threads, we introduce an explicit set of sequential algorithms and empirically demonstrate their effectiveness. Our theoretical analysis proves that our algorithms achieve near-optimal computational complexity in certain cases. The techniques we develop are sufficiently rich to enable knockoff sampling in challenging models including cases where the covariates are continuous and heavy-tailed, and follow a graphical model such as the Ising model.

Date and Time: 
Tuesday, July 9, 2019 - 4:30pm
Venue: 
Sloan Mathematics Center, Room 380C

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

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