## CME 243: Risk Analytics and Management in Finance and Insurance (STATS 243)

Market risk and credit risk, credit markets. Back testing, stress testing and Monte Carlo methods. Logistic regression, generalized linear models and generalized mixed models. Loan prepayment and default as competing risks. Survival and hazard functions, correlated default intensities, frailty and contagion. Risk surveillance, early warning and adaptive control methodologies. Banking and bank regulation, asset and liability management. Prerequisite:
STATS 240 or equivalent.

Last offered: Summer 2016

## CME 245: Topics in Mathematical and Computational Finance

Description: Current topics for enrolled students in the MCF program: This course is an introduction to computational, statistical, and optimizations methods and their application to financial markets. Class will consist of lectures and real-time problem solving. Topics: Python & R programming, interest rates, Black-Scholes model, financial time series, capital asset pricing model (CAPM), options, optimization methods, and machine learning algorithms. Appropriate for anyone with a technical and solid applied math background interested in honing skills in quantitative finance. Prerequisite: basic statistics and exposure to programming.Can be repeated up to three times.

Last offered: Summer 2017
| Repeatable
3 times
(up to 3 units total)

## CME 249: Using Design for Effective Data Analysis

Teams of students use techniques in applied and computational mathematics to tackle problems with real world data sets. Application of design methodology adapted for data analysis will be emphasized; leverage design thinking to come up with efficient and effective data driven insights; explore design thinking methodology in small group setting.;apply design thinking to a specific data centric problem and make professional group presentation of the results. Limited enrollment. Prerequisites:
CME100/102/104 or equivalents, or instructor consent. Recommended:
CME106/108 and familiarity with programming at the level of
CME 192/193.

Last offered: Winter 2016

## CME 250: Introduction to Machine Learning

A Short course presenting the principles behind when, why, and how to apply modern machine learning algorithms. We will discuss a framework for reasoning about when to apply various machine learning techniques, emphasizing questions of over-fitting/under-fitting, regularization, interpretability, supervised/unsupervised methods, and handling of missing data. The principles behind various algorithms--the why and how of using them--will be discussed, while some mathematical detail underlying the algorithms--including proofs--will not be discussed. Unsupervised machine learning algorithms presented will include k-means clustering, principal component analysis (PCA), and independent component analysis (ICA). Supervised machine learning algorithms presented will include support vector machines (SVM), classification and regression trees (CART), boosting, bagging, and random forests. Imputation, the lasso, and cross-validation concepts will also be covered. The R programming language will be used for examples, though students need not have prior exposure to R. Prerequisite: undergraduate-level linear algebra and statistics; basic programming experience (R/Matlab/Python).

Last offered: Spring 2020

## CME 250A: Machine Learning on Big Data

A short course presenting the application of machine learning methods to large datasets.Topics include: brief review of the common issues of machine learning, such as, memorizing/overfitting vs learning, test/train splits, feature engineering, domain knowledge, fast/simple/dumb learners vs slow/complex/smart learners; moving your model from your laptop into a production environment using Python (scikit) or R on small data (laptop sized) at first; building math clusters using the open source H2O product to tackle Big Data, and finally to some model building on terabyte sized datasets. Prereqresites: basic knowledge of statistics, matrix algebra, and unix-like operating systems; basic file and text manipulation skills with unix tools: pipes, cut, paste, grep, awk, sed, sort, zip; programming skill at the level of CME211 or
CS106A.

Last offered: Spring 2016

## CME 250Q: Introduction to Quantum Computing and Quantum Algorithms

This course will cover the basic formalism of quantum states and quantum measurements, and introduce the circuit model of quantum computation. Basic results such as the Solovay-Kitaev theorem, no-cloning theorem, quantum entanglement and Bell's inequality will be discussed followed by the quantum Fourier transform (QFT) and quantum phase estimation (QPE), and cover some of its important applications such as the celebrated Shor's algorithm for integer factorization (other applications will be mentioned but not discussed in detail), Grover's algorithm for quantum search is covered next, and lower bounds for query complexity in this context; some basic concepts of quantum error correction and quantum entropy, distance between quantum states, subadditivity and strong subadditivity of von Neumann quantum entropy will also be covered. Time permitting, we will discuss some advanced algorithms such as the HHL algorithm for matrix inversion, VQE (variational quantum eigensolver) and the QAOA al
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This course will cover the basic formalism of quantum states and quantum measurements, and introduce the circuit model of quantum computation. Basic results such as the Solovay-Kitaev theorem, no-cloning theorem, quantum entanglement and Bell's inequality will be discussed followed by the quantum Fourier transform (QFT) and quantum phase estimation (QPE), and cover some of its important applications such as the celebrated Shor's algorithm for integer factorization (other applications will be mentioned but not discussed in detail), Grover's algorithm for quantum search is covered next, and lower bounds for query complexity in this context; some basic concepts of quantum error correction and quantum entropy, distance between quantum states, subadditivity and strong subadditivity of von Neumann quantum entropy will also be covered. Time permitting, we will discuss some advanced algorithms such as the HHL algorithm for matrix inversion, VQE (variational quantum eigensolver) and the QAOA algorithm for optimization. Requires programming in Python, where the goal will be to familiarize the students to available software for quantum algorithm development, existing libraries, and also run some simple programs on a real quantum computer. Prerequisites: Linear algebra at the level of
CME 200 /
MATH 104, basic knowledge of group theory, and programming in Python. Additionally, some knowledge of real analysis will be helpful.

Last offered: Autumn 2019

## CME 251: Geometric and Topological Data Analysis (CS 233)

Mathematical and computational tools for the analysis of data with geometric content, such images, videos, 3D scans, GPS traces -- as well as for other data embedded into geometric spaces. Linear and non-linear dimensionality reduction techniques. Graph representations of data and spectral methods. The rudiments of computational topology and persistent homology on sampled spaces, with applications. Global and local geometry descriptors allowing for various kinds of invariances. Alignment, matching, and map/correspondence computation between geometric data sets. Annotation tools for geometric data. Geometric deep learning on graphs and sets. Function spaces and functional maps. Networks of data sets and joint learning for segmentation and labeling. Prerequisites: discrete algorithms at the level of
CS161; linear algebra at the level of Math51 or
CME103.

Terms: Spr
| Units: 3

Instructors:
Guibas, L. (PI)
;
Rempe, D. (TA)

## CME 253: Introduction to GPU Computing and CUDA

Covers the fundamentals of accelerating applications with GPUs (Graphics Processing Units); GPU programming with CUDA and OpenACC, debugging, thrust/CUB, profiling, optimization, debugging, and other CUDA tools. Libraries to easily accelerate compute code will be presented and deployment on larger systems will be addressed, including multi-GPU environments. Several practical examples will be detailed, including deep learning. Pre-requiste: knowledge of C/C++ at the level of CME211 or
CS106b.

Last offered: Winter 2017

## CME 257: Advanced Topics in Scientific Computing with Julia

This course will rapidly introduce students to the Julia programming language, with the goal of giving students the knowledge and experience necessary to navigate the language and package ecosystem while using Julia for their own scientific computing needs. The course will begin with learning the basics of Julia, and then introduce students to git version control and package development. Additional topics include: common packages, parallelism, interfacing with shared object libraries, and aspects of Julia's implementation (e.g. core numerical linear algebra). Lectures will be interactive, with an emphasis on collaboration and learning by example. Prerequisites: Data structures at the level of
CS106B, experience with one or more scientific computing languages (e.g. Python, Matlab, or R), and some familiarity with the Unix shell. No prior experience with Julia or git is required.

Last offered: Autumn 2019

## CME 262: Imaging with Incomplete Information (CEE 362G)

Statistical and computational methods for inferring images from incomplete data. Bayesian inference methods are used to combine data and quantify uncertainty in the estimate. Fast linear algebra tools are used to solve problems with many pixels and many observations. Applications from several fields but mainly in earth sciences. Prerequisites: Linear algebra and probability theory.

Terms: Spr
| Units: 3-4

Instructors:
Kitanidis, P. (PI)
;
Zhou, Z. (TA)

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