3,464 Works

UBC Congregation Ceremony [1996_05_30_am]

University Of British Columbia Ceremonies And Events Office

Computational statistical methods applied on conducting scientific literature reviews

Igor Barahona
In the last two decades the number of published articles and the amount of digital information has grown exponentially. This perspective increases the complexity on performing accurate and objective literature reviews. In this talk, a novel methodology based on computational statistics is introduced for investigating datasets composed by abstracts of published articles. We address to questions such as how is vocabulary commonly used in science What are the most relevant topics for the studied journals...

Importance sampling with nonequilibrium trajectories

Eric Vanden-Eijnden
Sampling with a dynamics that breaks detailed balance poses a challenge because the steady state probability is not typically known. In some cases, most notably in uses of the Jarzynski estimator in statistical physics, astrophysics, and machine learning, it is possible to estimate an equilibrium average using nonequilibrium dynamics. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations that have been transported by nonequilibrium trajectories. Our approach can be...

On the hypocoercivity of some PDMP-Monte Carlo algorithms

Christophe Andrieu
Monte Carlo methods based on Piecewise Deterministic Markov Processes (PDMP) have recently received some attention. In this talk we discuss (exponential) convergence to equilibrium for a broad sub-class of PDMP-MC, covering Randomized Hamiltonian Monte Carlo, the Zig-Zag process and the Bouncy Particle Sampler as particular cases, establishing hypocoercivity under fairly weak conditions and explicit bounds on the spectral gap in terms of the parameters of the dynamics. This allows us, for example, to discuss dependence...

Monte Carlo sampling of rare events in diffusive dynamical systems

David P. Sanders
(joint work with Diego Tapias, David P. Sanders, Eduardo G. Altmann)

Thermodynamic formalism, functional inequalities and model-form UQ for stochastic processes.

Luc Rey-Bellet
How do you ascertain the uncertainty associated with your favorite (ergodic) Markov process Suppose for example you are interested in computing steady-state expectations of some observable for the process. If think of this process as an idealized (or approximate) version of the true, but unknown, process, can we obtain performance guarantees on the steady state expectation for the true system To do this we will investigate what are the good measures of "distance" between stochastic...

A Constructive Approach to PDMPs

Samuel Power
Piecewise-Deterministic Markov Processes (PDMPs) have attracted attention in recent years as a non-reversible alternative to traditional reversible MCMC methods. By using a combination of deterministic dynamics and jump processes, these methods are often able to suppress random-walk behaviour and reach equilibrium rapidly. Although the PDMP framework accommodates at wide range of underlying dynamics in principle, existing approaches have tended to use quite simple dynamics, such as straight lines and elliptical orbits. In this work, I...

Beyond Well-Tempered Metadynamics algorithms for sampling multimodal target densities

Gersende Fort
In many situations, sampling methods are considered in order to compute expectations with respect to a distribution $\pi \, d\lambda$ on $X \subset \mathbb{R}^D$ , when $\pi$ is highly multimodal. Free-energy based adaptive importance sampling techniques have been developed in the physics and chemistry literature to efficiently sample from such a target distribution. These methods are casted in the class of adaptive Markov chain Monte Carlo (MCMC) samplers: at each iteration, a sample approximating a...

Simulated Tempering Method in the Infinite Switch Limit with Adaptive Weight Learning

Anton Martinsson
We discuss sampling methods based on variable temperature (simulated tempering). We show using large deviation theory (and following the technique of [Plattner et al, JCP, 2011]) that the most efficient approach in simulated tempering is to vary the temperature infinitely rapidly over a continuous range. In this limit, we can replace the equations of motion for the temperature by averaged equations, with a rescaling of the force in the equations of motion. We give a...

High-dimensional Bayesian inference and convex geometry: theory, methods, and algorithms

Marcelo Pereyra
This presentation summarises some new developments in theory, methods, and algorithms for performing Bayesian inference in high-dimensional models that are log-concave, with application to mathematical and computational imaging in convex settings. These include new efficient stochastic simulation and optimisation Bayesian computation methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty...

Fast randomized iterative numerical linear algebra for quantum chemistry and other applications

Jonathan Weare
I will discuss a family of recently developed stochastic techniques for linear algebra problems involving massive matrices. These methods can be used to, for example, solve linear systems, estimate eigenvalues/vectors, and apply a matrix exponential to a vector, even in cases where the desired solution vector is too large to store. The first incarnations of this idea appear for dominant eigenproblems arising in statistical physics and in quantum chemistry and were inspired by the real...

Duality of estimation and control and its application to rare event simulation

Carsten Hartmann
Many complex systems studied by scientists and engineers are characterised by processes that take place on vastly different time scales. Often the interesting system behaviour, such as phase transitions or regime changes, happens on the longest time scales, and the precise statistical estimation of these slow processes or associated rare events is among the most challenging computational problems in science and engineering. The talk will be devoted to the question of computing the optimal change...

Sequential Monte Carlo for Bayesian Analysis of Spectroscopy

Matt Moores
The spectral signature of a molecule can be predicted using a quantum-mechanical model, such as time-dependent density functional theory (TD-DFT). However, there are no uncertainty estimates associated with these predictions, and matching with peaks in observed spectra is often performed by eye. This talk introduces a model-based approach for baseline estimation and peak fitting, using TD-DFT predictions as an informative prior. The peaks are modelled as a mixture of Lorentzian, Gaussian, or pseudo-Voigt broadening functions,...

Gibbs flow transport for Bayesian inference

Jeremy Heng
In this work, we consider the construction of transport maps between two distributions using flows. In the Bayesian formalism, this ordinary differential equation approach is natural when one introduces a curve of distributions that connects the prior to posterior by tempering the likelihood. We present a novel approximation of the resulting partial differential equation which yields an ordinary differential equation whose drift depends on the full conditional distributions of the posterior. We discuss properties of...

(Hands-on + discussion) Scaling limits for modern MCMC algorithms

Roberts, Gareth 0.
The presentation will review results on infinite dimensional limits for some modern MCMC algorithms with a particular focus on Piecewise Deterministic Markov Processes PDMPs. The talk will also discuss the methodological consequences of these results for MCMC implementation. For certain stylised sequences of target density and particular MCMC algorithms, limit results can be obtained as the dimension of the target diverges. For traditional (Metropolis-Hastings type) MCMC algorithms, such limits are typically (but not always) diffusions....

Numerical integration within the Hamiltonian (Hybrid) Monte Carlo method

Jesús María Sanz-Serna
The Hamiltonian or Hybrid Monte Carlo (HMC) method is a valuable sampling algorithm used in both molecular dynamics and statistics. Its efficiency very much depends on the numerical integration of the dynamics employed to define the proposal, with Verlet/leapfrog being the algorithm of choice. In the talk I will discuss how different properties of the integrator impact the efficiency of HMC and how to construct novel integrators that significantly improve on Verlet. I will also...

Metastability in molecular dynamics and Bayesian inference methods

Florian Maire
Metastability is a phenomenon that concerns both molecular dynamic (and in particular protein dynamic) and Bayesian inference, especially when the posterior distribution of interest is multimodal. Restricting our focus to Markov processes and Markov chains, we explore this duality and study how Bayesian inference methods can benefit from practices developed in protein dynamic analysis and conversely. Questions of interest include the characterization and consequences of metastability in both perspectives. A particular attention will be given...

Quasisymmetric Macdonald Polynomials

Elizabeth Niese
My main research focus right now is symmetric and quasisymmetric functions. In particular, I am interested in specializations of Macdonald polynomials and generalizations of Schur functions. A symmetric function is a polynomial which remains unchanged when the variables are permuted. The Schur function basis for symmetric functions is related to many different areas of mathematics and can be generated in many ways, but I am most interested in its combinatorial aspects and the properties of...

Statistical approach for investigating change in mutational process during cancer growth and development.

Kimberly Siegmund
Human cancer somatic mutations arise from a variety of biological processes. Different processes produce different patterns of somatic mutations called mutation signatures. Tumor growth, just like phylogeny and human development, requires genome replication, which generates intratumor heterogeneity from replication errors. Early somatic mutations accumulated between the zygote and the first initiating tumor cell should appear in all descendant cells, and those that appear later in growth, in progressively smaller subsets. These are called trunk and...

Integrated genomic analyses of ovarian cancer cell lines to predict drug sensitivity.

Rob Scharpf
To improve our understanding of ovarian cancer, we performed genome-wide analyses of 45 ovarian cancer cell lines. Given the challenges of genomic analyses of tumors without matched normal samples, we developed approaches for detection of somatic sequence and structural changes and integrated these with epigenetic and expression alterations. Alterations not previously implicated in ovarian cancer included amplification or overexpression of ASXL1 and H3F3B, deletion or underexpression of CDC73 and TGF beta receptor pathway members, and...

Integrative genomic analyses of TCGA pan-cancer data.

Katherine Hoadley
The Cancer Genome Atlas has culminated over a decade of work characterization over 11,000 tumors from 33 different tumor types in a large scale, multidimensional data analysis called the PanCancer Atlas. This multi-institutional project resulted in 26 papers under three main themes â Cell of Origin, Oncogenic Processes, and Signaling Pathways. In the Cell of Origin marker paper, we explored the molecular classification of samples by chromosome arm level aneuploidy, DNA methylation, mRNA, miRNA, and...

Mutational dynamics in the mouse mitochondrial genome.

Maribel Hernández Rosales
In the cell there are from hundreds to thousands of mitochondria. Mitochondrial mutant genomes can coexist with wild-type genomes. Mutations in the mitochondrial genome have been associated to several diseases, such as aging, Alzheimerâ s disease, Parkinsonâ s disease, some forms of cancer, infertility, neuromuscular disorders, etc. In this work, we address the following questions: what is the mutation load in the mitochondrial genome does the mutation load change in the mouse brain in different...

Detection of de novo copy number deletions from targeted sequencing of trios

Ingo Ruczinski
De novo copy number deletions have been implicated in many diseases, but no formal methods existed that identify de novo deletions in parent-offspring trios from capture-based sequencing platforms. We developed Minimum Distance for Targeted Sequencing (MDTS) to fill this void. MDTS has similar sensitivity (recall), but a much lower false positive rate compared to less specific CNV callers, resulting in a much higher positive predictive value (precision). MDTS also exhibited much better scalability. We applied...

Combining heterogeneous genomics data to understand complex human traits.

Sara Mostavafi
Recent availability of large-scale multi-omics datasets from human cohort studies present new opportunities for deriving molecular mechanisms for complex disease. However, a central challenge in using these genomics data to understand complex traits is to disentangle causal, and hence reproducible and meaningful associations, from merely correlated ones. In this talk, Iâ ll describe ongoing projects that develop new statistical and computational methods for integrative analysis of multi-omics data, with the ultimate goal of providing insights...

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