linear-models   38

Common statistical tests are linear models (or: how to teach stats)
Most of the common statistical models (t-test, correlation, ANOVA; chi-square, etc.) are special cases of linear models or a very close approximation. This beautiful simplicity means that there is less to learn. In particular, it all comes down to y=a⋅x+b which most students know from highschool. Unfortunately, stats intro courses are usually taught as if each test is an independent tool, needlessly making life more complicated for students and teachers alike.
statistics  linear-models  inference  statistical-tests 
11 weeks ago by tarakc02
[1902.06720] Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent
A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we show that for wide neural networks the learning dynamics simplify considerably and that, in the infinite width limit, they are governed by a linear model obtained from the first-order Taylor expansion of the network around its initial parameters. Furthermore, mirroring the correspondence between wide Bayesian neural networks and Gaussian processes, gradient-based training of wide neural networks with a squared loss produces test set predictions drawn from a Gaussian process with a particular compositional kernel. While these theoretical results are only exact in the infinite width limit, we nevertheless find excellent empirical agreement between the predictions of the original network and those of the linearized version even for finite practically-sized networks. This agreement is robust across different architectures, optimization methods, and loss functions.
neural-net  linear-models  gradient-descent 
february 2019 by arsyed

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