Add gradient descent docs

[rsenne]

Adds a documentation example to resolve #51. Adds two examples 1.) fitting an hmm inside EM with GD and 2.) fitting an HMM by using autodiff + GD over all parameters. Let me know how this looks! happy to make changes

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EDIT by @gdalle:

• Bumped Julia lower bound to 1.10
• Bumped package version to 0.7.1

[Copilot]

Pull request overview

This PR adds comprehensive documentation examples demonstrating two approaches for fitting HMMs using gradient descent, resolving issue #51. The tutorial covers: (1) using gradient-based optimization within the EM algorithm for observation models without closed-form updates, and (2) end-to-end gradient-based fitting of all HMM parameters using automatic differentiation with the forward algorithm.

• Implements a custom NormalModel observation model with gradient-based fit! method using BFGS optimization
• Demonstrates fitting HMMs via Baum-Welch EM with gradient descent in the M-step for observation parameters
• Shows how to optimize all HMM parameters jointly using autodiff over the forward algorithm's log-likelihood

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 4 comments.

File	Description
examples/gradientdescent.jl	New tutorial file demonstrating gradient descent approaches for HMM fitting with comprehensive examples and tests
docs/make.jl	Adds the gradient descent tutorial to the documentation build configuration
docs/Project.toml	Adds Optim.jl dependency for documentation examples
test/Project.toml	Adds Optim.jl dependency for running tutorial tests

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.28%. Comparing base (39ae66b) to head (f9dff3f).

Additional details and impacted files

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  Coverage   95.28%   95.28%           
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  Files          18       18           
  Lines         509      509           
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  Hits          485      485           
  Misses         24       24           

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[gdalle]

I like the idea very much! Here are a few suggestions, thank you for the initiative

[rsenne]

Test for current version of Julia failed as Optim has API changes in recent breaking version 2.0.0. I changed tutorial to reflect this new API. All other tests pass locally