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#1




Machine Learning and Pattern Recognition Thread  starting 12/15/17
This will be a very theorydriven study. If you're just interested in running code and none of the theory, I would recommend you look elsewhere. There are many books and resources that serve this purpose.
I'm taking a gradlevel statistical machine learning course next semester and am trying to learn this material ahead of time. My goal is mainly to learn the theory, with implementing the algorithms in R (maybe some Python) on the side. Here are the books I'll be using, roughly from highest to lowest emphasis (primary texts in bold): Machine Learning: A Bayesian and Optimization Perspective (Theodoridis) Pattern Recognition (Theodoridis) Pattern Recognition and Neural Networks (Ripley) Pattern Recognition and Machine Learning (Bishop) Foundations of Machine Learning (Mohri et al.) Understanding Machine Learning (ShalevShwartz, BenDavid) HandsOn Machine Learning with ScikitLearn and Tensorflow (Geron) Machine Learning (Flach) Make Your Own Neural Network (Rashid) Modern Multivariate Statistical Techniques (Izenman) Principles and Theory for Data Mining and Machine Learning (Clarke et al.) Elements of Statistical Learning (Hastie et al.) Machine Learning (Murphy) Learning from Data (AbuMostafa et al.) Introduction to Statistical Learning (James et al.) Practical Data Science with R (Zumel, Mount) Python Machine Learning (Raschka) Applied Predictive Modeling (Johnson, Kuhn) Bayesian Methods for Data Analysis (Carlin, Louis) Generalized Additive Models (Wood) Matrix Computations 4th ed. (Golub, Van Loan) Convex Optimization (Boyd, Vandenberghe) I will be starting with the Machine Learning text by Theodoridis, and then proceed to the Pattern Recognition text when finished with the ML text. I will also post blog posts explaining the concepts as I learn them, as well as code in primarily R (maybe Python) where appropriate. This will be the main thread for discussion on these concepts. I will not have a predetermined schedule, but will try to cover concepts as quickly as possible. I'm going to assume that you are proficient with probability (examP level is fine), linear algebra, and mathematical statistics at an undergraduate level and will not spend any time reviewing this material. However, if you have any questions on the material, please feel free to ask in this thread.
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If you want to add me on LinkedIn, PM me. Why I hate Microsoft Access. Studying/Reading: Machine Learning and Pattern Recognition Last edited by clarinetist; 12102017 at 03:28 PM.. 
#2




Section 2.2.4, on complex random variables: http://ymmathstat.blogspot.com/2017/...variables.html
Sections 2.4 and prior should be mostly review (or slight extensions) of examP material.
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If you want to add me on LinkedIn, PM me. Why I hate Microsoft Access. Studying/Reading: Machine Learning and Pattern Recognition 
#3




I’d say that I think most of this syllabus ties back to computational complexity with the understanding that, subject to some feasibility conditions, generalized inference is an NP optimization problem (and I’ll speculate that it’s NP complete as well).
A complex random variable shouldn’t be much more problematic than a vector valued random variable. I’ve had to work with complex scalars in a quantum computing course and the way it worked was that the formalism had too many degrees of freedom to represent the system but you basically either add a constraint to compensate or you identify what values of the variables need to be treated as physically indistinguishable. Complex scalars give linear algebra a little more oomph in terms of being able to treat more phenomena as purely linear. You can, of course, represent complex numbers as matrices and linear transformations on them can correspondingly be block matrices but making them scalars emphasizes that the same math can be used for the full range of phenomena. 
#5




I've never seen complex random variables in the context of machine learning. What's the connection here?

#6




Stay tuned, I'm still trying to figure that out. It appears that they're being referred to throughout the text.
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If you want to add me on LinkedIn, PM me. Why I hate Microsoft Access. Studying/Reading: Machine Learning and Pattern Recognition 
#8




The largest absolute value component of an FFT run on a music sample gives you an estimate of the beats per minute of the music. If you bootstrap the sample in a manner that preserves the frequencies that you're interested in, you can get a distribution of spectra that should contain more inferred features.
Or, let's say you take a greyscale image of text and generate random line segments and run an FFT on the greyscale values that intersect with the line segment, you should get a distribution of spectra that relates to the presence of features defined by the relative distance of dark/light pixels that would not be sensitive to orientation of the text. If you give the line segments a distribution of measures that gives them coverage of adjustments for viewing text from different angles, it could reduce sensitivity to different viewing angles. I'm not sure how efficient either of these concepts would be, but they seem like they should pick up some feature inferences. 
#9




A more efficient version if that second concept is outlined here:
http://wwwsigproc.eng.cam.ac.uk/fos...sApps_UDRC.pdf Actually some of this ties back to observations of animal vision systems. Presence of very simple features that can be read with a kernel density estimator or wavelet correspond with the firing of specific neurons in animal studies. 
#10




Fourier methods use complex numbers, but to the best of my knowledge they don't specifically rely on complex random variables.
I found a CAS note that describes complex random variables and some potential actuarial applications. I don't know how mainstream those ideas are or will be, but odds are good that someone will find it useful. 
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