Contents

Introduction

Introduction

In this chapter, we do blah. Specifically

  • foo

  • bar.

  • baz

For more details, see HMMs index and HMM chapter and HMMs index and [Sar13].

What are state space models?

Python

We’re now ready to start coding.

from matplotlib import rcParams, cycler
import matplotlib.pyplot as plt
import numpy as np
plt.ion()

# Fixing random state for reproducibility
np.random.seed(19680801)

N = 10
data = [np.logspace(0, 1, 100) + np.random.randn(100) + ii for ii in range(N)]
data = np.array(data).T
cmap = plt.cm.coolwarm
rcParams['axes.prop_cycle'] = cycler(color=cmap(np.linspace(0, 1, N)))


from matplotlib.lines import Line2D
custom_lines = [Line2D([0], [0], color=cmap(0.), lw=4),
                Line2D([0], [0], color=cmap(.5), lw=4),
                Line2D([0], [0], color=cmap(1.), lw=4)]

fig, ax = plt.subplots(figsize=(10, 5))
lines = ax.plot(data)
ax.legend(custom_lines, ['Cold', 'Medium', 'Hot']);
../_images/intro-chap_2_0.png 
import matplotlib.pyplot as plt
import numpy as np
import jax
import jax.numpy as jnp

print(jax.devices())

WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)

[CpuDevice(id=0)]

Images

../_images/cat_dog.jpg

Fig. 1 A photo of a cat and a dog.

../_images/cat_dog.jpg

Fig. 2 Another photo of a cat and a dog.

In Figure 1 we show catdog. In Figure 2 we show catdog2, its twin.

Math

We have \(E= mc^2\), and also

(1)\[a x^2 + bx+ c = 0\]

From (1), it follows that $\( \begin{align} 0 &= a x^2 + bx+ c \\ 0 &= a x^2 + bx+ c \end{align} \)$

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State Space Models: A Modern Approach

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