Note Nov 2021
Reinforcement Learning
Training via exploration
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THE ARCHIVE
All Notes
Every technical note, derivation, and definition in the archive. Filter by subject, or choose Reference for the shorter supporting pieces.
Note Oct 2021
Parameter Space and Data Space
Characterizing Two Fundamental Spaces in Data Science
Definition Oct 2021
Induced Norm
The definition of an induced matrix norm and how it measures the largest stretch a linear map can apply.
Note Oct 2021
Matrix Norms
Measuring the size of the transformation described by a matrix.
Note Oct 2021
Minimum Norm Problem
Choosing the best estimate from a set of feasible solutions.
Note Oct 2021
Weighted Minimum Norm Problem
Generalization of Minimum Norm Problem
Note Oct 2021
Forward-Backward Linear Predictor (FBLP)
Improving the efficiency of our prediction.
Note Oct 2021
Simple Least-Squares Filtering
Simple filter problem
Note Oct 2021
The Gram Matrix and Normal Equations
The orthogonality condition
Note Oct 2021
Best predictor to minimize absolute deviation.
The expected absolute error is minimized when the prediction is the median of the observations.
Note Oct 2021
Visualizing Models with Known Functional Form
Intro to data space and parameter space.
Note Oct 2021
Intro to Loss Functions
Which one is appropriate for the task at hand?
Note Oct 2021
The Modeling Tradeoff
Minimize biasedness, variance, or MSE?
Derivation Aug 2021
Zero Conditional Mean Implies Zero Covariance
Why a zero conditional mean implies that the disturbance is uncorrelated with the regressors.
Note Aug 2021
OLS Unbiasedness
Recovering population parameters for β.
Derivation Aug 2021
M₀: The Deviation-from-Mean Matrix
How the deviation-from-mean matrix is constructed and what it does.
Note Aug 2021
The Effect of Including a Constant Column in OLS
Deviations from means.
Derivation Aug 2021
Derivation of the Variance of the Sample Mean
A compact derivation of the variance of the sample mean.
Note Aug 2021
Newey-West Covariance Matrix (Part 2)
The multivariate case of the Newey-West covariance matrix.
Note Jul 2021
Central Limit Theorem (CLT)
The most prolific result in statistics.
Note Jul 2021
Newey-West Covariance Matrix (Part 1)
A covariance matrix that incorporates heteroskedasticity and autocorrelation.
Note Jul 2021
A Brief Introduction to Deep Learning
A bird's eye view of a tremendously deep field within machine learning.
Derivation Jun 2021
Partitioned Least Squares Derivation
Deriving the partitioned least-squares estimator by partialling out one block of regressors.
Derivation Jun 2021
Normal Equations for Partitioned Least Squares
The full derivation of the normal equations for partitioned least squares.
Derivation Jun 2021
The Beta Constraint for Active Portfolios
Why the beta of the benchmark component equals one, and what that implies for active weights.
Note Jun 2021
Benchmark Portfolio Optimization
Optimizing a portfolio relative to a respected benchmark.
Note Jun 2021
Providing an Active Portfolio
Supplying alpha to a benchmark portfolio.
Note Jun 2021
Solution for Constrained Weighted Least Squares
Full setup and solving for CWLS in the context of factor models.
Note Jun 2021
Partitioned Least Squares
Understanding what it means to "partial out" variable effects.
Definition Jun 2021
Projection Matrix
A short reference on projection matrices and why idempotence implies projection.
Note Jun 2021
Factor Models 101
A technique for approximating the covariance matrix.
Definition Jun 2021
Alpha
A working definition of alpha, its role in portfolio returns, and its formula relative to a benchmark.
Note Jun 2021
The Geometry of Ordinary Least Squares
Visualizing the workhorse model for regression analysis.