How to express hyperparameter distributions in Spearmint?

I'm trying to use Spearmint, the Bayesian optimization library, to tune hyperparameters for a machine learning classifier. My question is how does one express parameter search spaces that does not follow a uniform distribution?

From the project's github page, here is an example of how to set two uniformly distributed parameter search spaces:

"variables": {
    "X": {
        "type": "FLOAT",
        "size": 1,
        "min":  -5,
        "max":  10
    },
    "Y": {
        "type": "FLOAT",
        "size": 1,
        "min":  0,
        "max":  15
    }
}

How would we define a search space like the one below in Spearmint?

SVC_PARAMS = [
    {
        "bounds": {
            "max": 10.0,
            "min": 0.01,
        },
        "name": "C",
        "type": "double",
        "transformation": "log",
    },
    {
        "bounds": {
            "max": 1.0,
            "min": 0.0001,
        },
        "name": "gamma",
        "type": "double",
        "transformation": "log",
    },
    {
        "type": "categorical",
        "name": "kernel",
        "categorical_values": [
            {"name": "rbf"},
            {"name": "poly"},
            {"name": "sigmoid"},
        ],
    },
]

Is there a place to look up all of the stochastic expressions (ie uniform, normal, log etc) currently being supported by Spearmint?

Solution

Spearmint learns these kinds of transformations automatically from the data. If you take a look here: https://github.com/HIPS/Spearmint/tree/master/spearmint/transformations you can see the implementation of the beta warping that is applied (detailed in this paper: http://arxiv.org/abs/1402.0929). Spearmint doesn't have a way to specify these a-priori, but you could have Spearmint operate on e.g. the log of the parameters (by giving the log of the parameter ranges and exponentiating on your end).