AddTree Covariance Function

Dependencies

This project depends on george, numpy and scipy. george must be compiled manually.

git clone https://github.com/maxc01/george
cd george
python setup.py install

If you use poetry to manage dependencies, the following commands will install all dependencies and this project:

git clone https://github.com/maxc01/addtree
cd addtree
poetry install

Otherwise, you will have to install these dependencies manually. Section [tool.poetry.dependencies] in pyproject.toml lists all dependencies and their versions.

How to code a tree given an objective function

The first step is to represent an objective function at hand using a tree. For example, the synthetic function presented in Jenatton2017 can be encoded using a tree shown in the left part of the following figure and its corresponding code snippet is shown in the right part. We clarify this code snippet in the following.

1. root node doesn’t contain a continuous parameter, thus the dimension of this parameter is set to be zero
2. x2 node contains a one-dimensional continuous parameter, and this parameter is shared by two sub-functions associated with the first and second leaves (counting from left to right)
3. x5 node contains a one-dimensional continuous parameter
4. build tree dependencies by adding x7 as a child of x3
5. finish tree construction (precompute some quantities)

How to code a tree-structured function

The general rule of coding a tree-structured function is using a hierarchical dictionary as the parameter of this function. For example, the code snippet corresponding to the above tree-structured function is shown below.

def obj_func(params):
    SHIFT = 0.5

    if params["L1"]["cat_value"] == "left" and params["L2"]["cat_value"] == "left":
        value = (
            params["L1"]["cont_value"] + (params["L2"]["cont_value"] - SHIFT) ** 2 + 0.1
        )
    elif params["L1"]["cat_value"] == "left" and params["L2"]["cat_value"] == "right":
        value = (
            params["L1"]["cont_value"] + (params["L2"]["cont_value"] - SHIFT) ** 2 + 0.2
        )
    elif params["L1"]["cat_value"] == "right" and params["L2"]["cat_value"] == "left":
        value = (
            params["L1"]["cont_value"] + (params["L2"]["cont_value"] - SHIFT) ** 2 + 0.3
        )
    elif params["L1"]["cat_value"] == "right" and params["L2"]["cat_value"] == "right":
        value = (
            params["L1"]["cont_value"] + (params["L2"]["cont_value"] - SHIFT) ** 2 + 0.4
        )
    else:
        raise ValueError("parameter names are not correct")

    info = dict()
    info["value"] = value
    info["value_sigma"] = 1e-9
    return info

For a more complex tree-structured function, see the objective function of a simple NAS problem.

Examples

synthetic function (from Jenatton2017)

cd examples
python addtree_jenatton_small.py

log files will be located in exp_results/addtree/jenatton-small/a-unique-dir. The following figure shows comparison of different algorithms on optimizaing the synthetic function.

model compression

cd examples
python {{ algo }}_model_compression_multiple.py {{ model_name }} OUTPUT_PATH --pretrained PRETRAINED_PATH --prune_epochs 1

model_name can be “vgg16”, “resnet50” or “resnet56”. algo can be “addtree”, “random” , “tpe” or “smac”.

For example, to compress resnet50 using addtree,

python addtree_model_compression_multiple.py resnet50 OUTPUT_PATH --pretrained PRETRAINED_PATH --prune_epochs 1

The following picture shows comparison of different algorithms on compressing resnet50.

citation

@inproceedings{ma2020,
  title = {Additive {{Tree}}-{{Structured Covariance Function}} for {{Conditional Parameter Spaces}} in {{Bayesian Optimization}}},
  booktitle = {International {{Conference}} on {{Artificial Intelligence}} and {{Statistics}}},
  author = {Ma, Xingchen and Blaschko, Matthew},
  year = {2020},
  month = jun,
  pages = {1015--1025},
  publisher = {{PMLR}},
  issn = {2640-3498},
  language = {en}
}

@article{ma2020b,
  title = {Additive Tree-Structured Conditional Parameter Spaces in Bayesian Optimization: {{A}} Novel Covariance Function and a Fast Implementation},
  author = {Ma, X. and Blaschko, M. B.},
  year = {2020},
  publisher = {{IEEE Computer Society}},
  address = {{Los Alamitos, CA, USA}},
  issn = {1939-3539},
  doi = {10.1109/TPAMI.2020.3026019},
  journal = {IEEE Transactions on Pattern Analysis \& Machine Intelligence},
  keywords = {additives,bayes methods,data models,linear programming,mathematical model,neural networks,optimization}
}