Difference between revisions of "The Art of Scientific Research"

Revision as of 21:05, 13 August 2024

The Art of Scientific Research

This is a preparatory course for the main part of m1p.

Machine learning at one go
Linear models (and processes) with time (regression, SVD, PCA, NN)
Tensor indexing and decomposition, Tucker, HOSVD, TT (getting rid of time by constructing a state space)
Types of optimization (what is the gradient and Jacoby matrix)
Convolution is a linear operator, Fourier is a linear operator
Graph convolution, metric spaces (if possible)
Kernel methods and RKHS
Canonical correlation analysis and autoencoders
Bayesian inference and regularization, optimization
Model selection
Multimodeling (privilege, distilling, domain transfer)
Introduction to sampling and generative models

Goals for the next year are CaТ, NODE, SDE, Diffusion, Riemannian, Tensors as tensors, Advanced calculus, Clifford algebra, Homology

(long reading 2196 pages) Algebra, Topology, Differential Calculus, and Optimization Theory for Computer Science and Machine Learning by Jean Gallier and Jocelyn Quaintance, 2024. pdf, github
(fun reading) The Art of Scientific Investigation by W. I. B. Beveridge, 1957 pdf
Data-Driven Science and Engineering: Machine Learning, Dynamical Systems. and Control by S.L. Brunton and J. N. Kutz, 2019.
Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges by M.M. Bronstein, J. Bruna, T. Cohen, P. Veličković, 2021. arxiv
Deep Learning: Foundations and Concepts by C.M. Bishop, H. Bishop, 2024 version'06
Mathematics for Physicists: Introductory Concepts and Methods by A. Altland. J. von Delf, 2017 pdf
Mathematics for Machine Learning by M.P. Deisenroth, A.A. Faisal, C.S. Ong pdf

Check and develop your typing skills

Sat 9:30 – 10:50 zoom | Sept 7 14 21 28 | Now 5 12 19 26 | Oct 2 9 16 23 30 | Dec 7 14 21 28

@@ Line 22: / Line 22: @@
 # Tell about a scientific society
 # Reproducible computational experiment
-# Computer supported brainstorming
+# Computer-supported brainstorming
-# Conferences and journals, review and schedules
+# Conferences and journals, review, and schedules
 # Writing a grant proposal
+==The theory to discuss==
+# Machine learning at one go
+# Linear models (and processes) with time (regression, SVD, PCA, NN)
+# Tensor indexing and decomposition, Tucker, HOSVD, TT (getting rid of time by constructing a state space)
+# Types of optimization (what is the gradient and Jacoby matrix)
+# Convolution is a linear operator,  Fourier is a linear operator
+# Graph convolution, metric spaces (if possible)
+# Kernel methods and RKHS
+# Canonical correlation analysis and autoencoders
+# Bayesian inference and regularization, optimization
+# Model selection
+# Multimodeling (privilege, distilling, domain transfer)
+# Introduction to sampling and generative models
+* Goals for the next year are CaТ, NODE, SDE, Diffusion, Riemannian, Tensors as tensors, Advanced calculus, Clifford algebra, Homology
 ==Scoring==