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"Kevin Murphy’s book on machine learning is a superbly written, comprehensive treatment of the field, built on a foundation of probability theory. It is rigorous yet readily accessible, and is a must-have for anyone interested in gaining a deep understanding of machine learning."
Kevin Murphy has a phenomenal ability to go deep while making topics digestible to a broad audience. His writing is clear and concise with great visuals throughout. I highly recommend this as "the book" for anyone wanting to become a well-versed ML expert."
“Probabilistic machine learning”: a book series by Kevin Murphy . Book 0: “Machine Learning: A Probabilistic Perspective” (2012) See this link. Book 1: “Probabilistic Machine Learning: An Introduction” (2022) See this link. Book 2: “Probabilistic Machine Learning: Advanced Topics” (2023) See
by Kevin Patrick Murphy. MIT Press, 2012. Key links. Buy hardcopy from MIT Press; Buy hardcopy from Amazon.com; Winner of De Groot prize in 2013 for best book in Statistical Science. Table of contents; Matlab software; All the figures, together with links to the Matlab code to regenerate them. Request solution manual (instructors only) Endorsements
A state space model or SSM is a partially observed Markov model, in which the hidden state, x t, evolves over time according to a Markov process, possibly conditional on external inputs or controls u t, and each hidden state generates some observations y t at each time step.
whereweusedthedefinitionoftheGammafunctionandthefactthat( x+ 1) = x( x). Wecanfindthevarianceinthesameway,byfirstshowingthat E 2 = ( a+ b) ( a)( b)
This chapter introduces state space models (SSMs). What are State Space Models? Hidden Markov Models. Linear Gaussian SSMs. Nonlinear Gaussian SSMs.
State Space Models: A Modern Approach. This is an interactive textbook on state space models (SSM) using the JAX Python library. Some of the content is covered in other books such as [Sar13] and [Mur23]. However, we go into more detail, and focus on how to efficiently implement the various algorithms in a “modern” computing environment ...
Suppose we observe N sequences D = {y n, 1: T n: n = 1: N}. Then the goal of parameter estimation, also called model learning or model fitting, is to approximate the posterior. (17) p (θ | D) ∝ p (θ) ∏ n = 1 N p (y n, 1: T n | θ) where p (y n, 1: T n | θ) is the marginal likelihood of sequence n:
We see that the observation matrix H simply ``extracts’’ the relevant parts of the state vector. Suppose we sample a trajectory and corresponding set of noisy observations from this model, (x 1: T, y 1: T) ∼ p (x, y | θ). (We use diagonal observation noise, R = diag (σ 1 2, σ 2 2).) The results are shown below.
