Mathematical forecasting - Revision history

Wiki: /* ICA */

2025-07-30T12:13:43Z

ICA

Wiki: /* ICA */

2025-07-30T11:56:06Z

ICA

Wiki: /* ICA */

2025-07-30T11:54:40Z

ICA

Wiki: /* Catch-up references */

2025-07-28T18:45:35Z

Catch-up references

Wiki: /* Motivation */

2024-10-07T20:14:06Z

Motivation

Wiki at 18:21, 15 September 2024

2024-09-15T18:21:12Z

Wiki: /* Intelligent Data Analysis 2024 */

2024-09-09T21:13:11Z

Intelligent Data Analysis 2024

Wiki: /* Intelligent Data Analysis 2024 */

2024-09-09T21:09:48Z

Intelligent Data Analysis 2024

Wiki: /* General */

2024-09-09T18:09:36Z

General

Wiki: /* Intelligent Data Analysis 2024 */

2024-09-04T11:36:04Z

Intelligent Data Analysis 2024

@@ Line 251: / Line 251: @@
 ===ICA===
 # Analysis of fMRI Data by Blind Separation Into Independent Spatial Components [https://papers.cnl.salk.edu/PDFs/Analysis%20of%20FMRI%20Data%20by%20Blind%20Separation%20Into%20Independent%20Spatial%20Components%201998-3633.pdf 1998]
 ===SSM===
 # Data-driven linearization of dynamical systems by Haller [https://www.georgehaller.com/reprints/datadrivenlinearization240815.pdf 2024]

@@ Line 250: / Line 250: @@
 ==Reference collection for 2025==
 ===ICA===
-# Analysis of fMRI Data by Blind Separation
+# Analysis of fMRI Data by Blind Separation Into Independent Spatial Components [https://papers.cnl.salk.edu/PDFs/Analysis%20of%20FMRI%20Data%20by%20Blind%20Separation%20Into%20Independent%20Spatial%20Components%201998-3633.pdf 1998]
 ===SSM===
 # Data-driven linearization of dynamical systems by Haller [https://www.georgehaller.com/reprints/datadrivenlinearization240815.pdf 2024]

@@ Line 251: / Line 251: @@
 ===ICA===
 # Analysis of fMRI Data by Blind Separation
-Into Independent Spatial Components  [https://papers.cnl.salk.edu/PDFs/Analysis%20of%20FMRI%20Data%20by%20Blind%20Separation%20Into%20Independent%20Spatial%20Components%201998-3633.pdf 1998]
+Into Independent Spatial Components [https://papers.cnl.salk.edu/PDFs/Analysis%20of%20FMRI%20Data%20by%20Blind%20Separation%20Into%20Independent%20Spatial%20Components%201998-3633.pdf 1998]
 ===SSM===
 # Data-driven linearization of dynamical systems by Haller [https://www.georgehaller.com/reprints/datadrivenlinearization240815.pdf 2024]

← Older revision		Revision as of 18:45, 28 July 2025
Line 247:		Line 247:
	# Manifolds, tensors, and forms by Paul Renteln, 2014 -->		# Manifolds, tensors, and forms by Paul Renteln, 2014 -->
	# Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Tailen Hsiing, Randall Eubank, 2013		# Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Tailen Hsiing, Randall Eubank, 2013
		+
		+	==Reference collection for 2025==
		+	===ICA===
		+	# Analysis of fMRI Data by Blind Separation
		+	Into Independent Spatial Components [https://papers.cnl.salk.edu/PDFs/Analysis%20of%20FMRI%20Data%20by%20Blind%20Separation%20Into%20Independent%20Spatial%20Components%201998-3633.pdf 1998]
		+	===SSM===
		+	# Data-driven linearization of dynamical systems by Haller [https://www.georgehaller.com/reprints/datadrivenlinearization240815.pdf 2024]

@@ Line 12: / Line 12: @@
 The course joins two parts of the problem statements in Machine Learning. The first part comes from the structure of the measured data. The data come from Physics, Chemistry, and Biology and have intrinsic algebraic structures. These structures are parts of the theory that stands behind the measurement. The second part comes from errors in the measurement. The stochastic nature of errors requires statistical methods of analysis. So this course joins algebra and statistics. It is devoted to the problem of predictive model selection.
-Mathematical forecasting methods play a crucial role in scientific research and industry. The distinction between forecasting and machine learning methods lies in the algebraic structures. We build forecasting models not only in vector spaces but also in vector fields. These fields include time and space and have a continuous nature. We propose a holistic approach to teaching this course: we must consider mathematical methods that combine continuous-time high-dimensional vector and tensor fields. We discuss linear, differential, and non-linear models. We introduce model ensembles to reveal both the source and the target space dependencies.
+Mathematical forecasting methods play a crucial role in scientific research and industry. The distinction between forecasting and machine learning methods lies in the algebraic structures. We build forecasting models not only in vector spaces but also in vector fields. These fields include time and space and have a continuous nature. We propose a holistic approach to teaching this course: we must consider mathematical methods that combine continuous-time high-dimensional vector and tensor fields. We discuss linear, differential, and non-linear models. We introduce model ensembles to reveal the source and target space dependencies.
 == Lectures ==

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   |description=This course delivers model selection methods in machine learning and forecasting. The models are linear, tensor, deep neural networks, and neural differential equations.
   }}
-==Intelligent Data Analysis 2024==
+The additional part moved to [[Functional Data Analysis]]
 ==Motivation==
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 '''[https://bit.ly/3QAOYPd Current labworks, October 2022, is here]'''
 Lab work contains a report in the pynb or TeX format and a talk with a discussion
-#Title and motivated abstract
+# Title and motivated abstract
-#Problem statement
+# Problem statement
-#Model, problem solution
+# Model, problem solution
-#Code, analysis, and illustrative plots
+# Code, analysis, and illustrative plots
 #References
-Note: '''the model''' is  the '''personal''' contribution. The infrastructure: data acquisition, data uploads, error functions, and plots are welcome to be created '''collectively''' and shared.
+Note: '''the model''' is the '''personal''' contribution. The infrastructure: data acquisition, data uploads, error functions, and plots are welcome to be created '''collectively''' and shared.
 ===Topics of the lab works (Fall)===
 *Autoregressive forecasting – Singular structure Analysis

@@ Line 8: / Line 8: @@
 [https://t.me/+2kCkkAyLbUxiOGQ6 The chat-link]
-Requirements for the talk:
+Requirements for the text and discussion (talk):
 # Comprehensive explanation of the method or the question we discuss
 # Only the principle, no experiments

@@ Line 27: / Line 27: @@
 # Generative CCA
 # Comparative analysis of variants of CCA like PLS and others
 ===General===
 # Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems [https://arxiv.org/abs/2307.08423 arxiv 2023]

@@ Line 31: / Line 31: @@
 # Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Machine Learning [https://www.cis.upenn.edu/~jean/math-deep.pdf upenn 2024]
 # The Elements of Differentiable Programming [https://arxiv.org/abs/2403.14606 arxiv 2024]
 ===Prerequisites===

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 # The list of references with doi
 # Tell how it was generated
-# Observing a gap, put a note about it
+# Observing a gap, put a note about it (to question later)
 === First series of questions  ===