They say loneliness breeds the best masters, and it’s awfully lonely at the top,”

# Gaussian Mixture Models.. GMMs

## Gaussian Mixture Models

- A probabilistic model
- Assumes all data points are generated from a mixture of finite no. of gaussian

distributions - The parameters of the gaussian distributions are unknown.
- It is a way of generalizing k-mean(or k-medoid or k-mode for that matter) clustering to use the

co-variance structure/stats as well as the mean/central-tendency measures of latent

gaussians.

## scikit-learn

- Implements the Expectation Maximization algorithm.

### Pros:

- Fastest for learning mixture models
- No bias of means towards zero, or bias cluster sizes to have specific structures

### Cons:

- When there’s not enough points per mixture, estimating covariance matrices becomes

difficult -
Number of components; will always use all the components it has access to, so might need

missing or test-reserved data.. -
No. of components can be chosen based on BIC criterion.

- Variational Bayesian Gaussian mixture avoids having to specify number of components

## Variational Bayesian Gaussian Mixture

- — Uses Variational Inference algorithm to estimate

## Fitting a Gaussian model to data

# Share:Worm

A similar problem on a smaller scale. I can walk through minutes, I could have walked back to save them, but I let them die because it meant a monster would remain gone. What merit is a gamble, a sacrifice, if you stake things that matter nothing to you?

# Share: Worm

have been doing this for ten years. I admire you for retaining your…” he trailed off.

“Idealism?”

“Not a word I’m familiar with, Weaver. Faith?”

“Faith works.”

“I have none left, after ten years. No faith. We are a wretched, petty species, and we have been given power to destroy ourselves with

# Factor Analysis — notes

## Multiple Classifications:

```
Aka [Dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction)
Aka
[Dimensionality Estimation] (http://disco.ethz.ch/lectures/fs11/seminar/paper/samuel-1.pdf)
### Methods:
* [Intrinsic Dimension Estimation](https://www.stat.berkeley.edu/~bickel/mldim.pdf)
or (http://www.sciencedirect.com/science/article/pii/S0020025515006179)
* [PCA](http://www.music.mcgill.ca/~ich/classes/mumt611_07/classifiers/lda_theory.pdf)
* [Kernel-PCA](http://papers.nips.cc/paper/1491-kernel-pca-and-de-noising-in-feature-spaces.pdf)
* [Graph-based kernel PCA](http://ieeexplore.ieee.org/abstract/document/1261097/)
* [Linear Discriminant Analysis](http://www.music.mcgill.ca/~ich/classes/mumt611_07/classifiers/lda_theory.pdfhttp://www.music.mcgill.ca/~ich/classes/mumt611_07/classifiers/lda_theory.pdf)
* [Generalized Discriminant Analysis](http://www.jmlr.org/papers/v6/ye05a.html)
* [Manifold Learning] (http://scikit-learn.org/stable/modules/manifold.html)
### Factor Analysis(based on goal):
* [Exploratory Factor
Analysis](https://en.wikipedia.org/wiki/Exploratory_factor_analysis):
#### Fitting Procedures:
* used to estimate factor loadings and unique variances
* [Confirmatory Factor
Analysis](https://en.wikipedia.org/wiki/Confirmatory_factor_analysis):
### Types of factoring:
* [Principal Component
Analysis](https://en.wikipedia.org/wiki/Principal_component_analysis):
* Canonical Factor Analysis: aka Rao's canonical factoring, uses principal axis
method, unaffected by arbitrary rescaling, highest canonical correlation measure.
* Common Factor Analysis: aka principal factor analysis, least no. of variables
accounting for the common variance of a set of variables.
* Image Factoring: based on correlation matrix of predicted variables, where each
prediction is done via [multiple
regression](https://en.wikipedia.org/wiki/Multiple_regression)
* Alpha Factoring: based on maximizing reliability of factors, assumes random
sampling of variables from universe of vars, (other methods assume fixed
variables)
* Factor Regression Model: Combinatorial model of factor and regression models,
aka hybrid factor model with partially known factors
### Terminology:
* Factor Loadings:
* Interpreting Factor loadings:
* Communality:
* Spurious Solutions:
* Uniqueness of Variable:
* EigenValues/Characteristic Roots:
* Extraction Sums of squared loadings:
* Factor Scores:
### Criteria for number of Factors:
* Horn's Parallel Analysis:
* Velicer's MAP test:
older methods
* Kaiser Criterion:
* Scree plot:
* Variance explained criteria:
### Rotation Methods:
* Varimax Rotation:
* Quartimax Rotation:
* Equimax Rotation:
* Direct oblimin Rotation:
* Promax Rotation:
```

# Why you need to improve your training data, and how to do it

Andrej Karpathy showed this slide as part of his talk at Train AI and I loved it! It captures the difference between deep learning research and production perfectly. Academic papers are almost entirely focused on new and improved models, with datasets usually chosen from a small set of public archives. Everyone I know who uses deep learning as part of an actual application spends most of their time worrying about the training data instead.

There are lots of good reasons why researchers are so fixated on model architectures, but it does mean that there are very few resources available to guide people who are focused on deploying machine learning in production. To address that, my talk at the conference was on “the unreasonable effectiveness of training data”, and I want to expand on that a bit in this blog post, explaining why data is so important…

View original post 3,917 more words

# The Bubble Under the Mathematical Rug

Don’t freak out, but we’re surrounded by normal distributions.

They’re in our heights; our weights; our sampling means; our fever-dreams; our Galton Boards…

Every normal is a variation on the same bell-curved theme. Just specify two parameters—the *mean*, i.e., the center of the distribution, and the *variance*, which measures its breadth—and you’ve got a normal distribution. They’re one big clan, with a strong family resemblance.

But—for me, at least—this raises a question: Who is the matriarch of the family? Which normal distribution is the founding member, the Mitochondrial Eve, the universal common ancestor?

View original post 825 more words

# The Battle of the Sexes is Bullshit: A Review of Stephen Marche’s The Unmade Bed (2018)

# Life on the Poincaré Disk

Just at this time I left Caen, where I was then living, to go on a geological excursion under the auspices of the school of mines. The changes of travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’ sake I verified the result at my leisure.

-Henri Poincaré,

Science and…

View original post 2,107 more words

# Matrix Jokes

*(NOTE: This is perhaps the dumbest post I’ve ever done. I couldn’t be prouder.)*