Features and Options

You likely don't need to tune the hyperparameters yourself, but if you would like, you can use hyperparamopt.py as an example.

Some configurable features and options in PySR which you may find useful include:

binary_operators, unary_operators
niterations
ncyclesperiteration
procs
populations
weights
maxsize, maxdepth
batching, batchSize
variable_names (or pandas input)
Constraining operator complexity
LaTeX, SymPy, and callable equation output
loss

These are described below

The program will output a pandas DataFrame containing the equations, mean square error, and complexity. It will also dump to a csv at the end of every iteration, which is hall_of_fame_{date_time}.csv by default. It also prints the equations to stdout.

Operators

A list of operators can be found on the operators page. One can define custom operators in Julia by passing a string:

equations = pysr.pysr(X, y, niterations=100,
    binary_operators=["mult", "plus", "special(x, y) = x^2 + y"],
    extra_sympy_mappings={'special': lambda x, y: x**2 + y},
    unary_operators=["cos"])

Now, the symbolic regression code can search using this special function that squares its left argument and adds it to its right. Make sure all passed functions are valid Julia code, and take one (unary) or two (binary) float32 scalars as input, and output a float32. This means if you write any real constants in your operator, like 2.5, you have to write them instead as 2.5f0, which defines it as Float32. Operators are automatically vectorized.

One should also define extra_sympy_mappings, so that the SymPy code can understand the output equation from Julia, when constructing a useable function. This step is optional, but is necessary for the lambda_format to work.

One can also edit operators.jl.

Iterations

This is the total number of generations that pysr will run for. I usually set this to a large number, and exit when I am satisfied with the equations.

Cycles per iteration

Each cycle considers every 10-equation subsample (re-sampled for each individual 10, unless fast_cycle is set in which case the subsamples are separate groups of equations) a single time, producing one mutated equation for each. The parameter ncyclesperiteration defines how many times this occurs before the equations are compared to the hall of fame, and new equations are migrated from the hall of fame, or from other populations. It also controls how slowly annealing occurs. You may find that increasing ncyclesperiteration results in a higher cycles-per-second, as the head worker needs to reduce and distribute new equations less often, and also increases diversity. But at the same time, a smaller number it might be that migrating equations from the hall of fame helps each population stay closer to the best current equations.

Processors

One can adjust the number of workers used by Julia with the procs option. You should set this equal to the number of cores you want pysr to use. This will also run procs number of populations simultaneously by default.

Populations

By default, populations=procs, but you can set a different number of populations with this option. More populations may increase the diversity of equations discovered, though will take longer to train. However, it may be more efficient to have populations>procs, as there are multiple populations running on each core.

Weighted data

Here, we assign weights to each row of data using inverse uncertainty squared. We also use 10 processes instead of the usual 4, which creates more populations (one population per thread).

sigma = ...
weights = 1/sigma**2

equations = pysr.pysr(X, y, weights=weights, procs=10)

Max size

maxsize controls the maximum size of equation (number of operators, constants, variables). maxdepth is by default not used, but can be set to control the maximum depth of an equation. These will make processing faster, as longer equations take longer to test.

One can warm up the maxsize from a small number to encourage PySR to start simple, by using the warmupMaxsize argument. This specifies that maxsize increases every warmupMaxsize.

Batching

One can turn on mini-batching, with the batching flag, and control the batch size with batchSize. This will make evolution faster for large datasets. Equations are still evaluated on the entire dataset at the end of each iteration to compare to the hall of fame, but only on a random subset during mutations and annealing.

Variable Names

You can pass a list of strings naming each column of X with variable_names. Alternatively, you can pass X as a pandas dataframe and the columns will be used as variable names. Make sure only alphabetical characters and _ are used in these names.

Constraining operator complexity

One can limit the complexity of specific operators with the constraints parameter. There is a "maxsize" parameter to PySR, but there is also an operator-level "constraints" parameter. One supplies a dict, like so:

constraints={'pow': (-1, 1), 'mult': (3, 3), 'cos': 5}

What this says is that: a power law x^y can have an expression of arbitrary (-1) complexity in the x, but only complexity 1 (e.g., a constant or variable) in the y. So (x0 + 3)^5.5 is allowed, but 5.5^(x0 + 3) is not. I find this helps a lot for getting more interpretable equations. The other terms say that each multiplication can only have sub-expressions of up to complexity 3 (e.g., 5.0 + x2) in each side, and cosine can only operate on expressions of complexity 5 (e.g., 5.0 + x2 exp(x3)).

LaTeX, SymPy, callables

The pysr command will return a pandas dataframe. The sympy_format column gives sympy equations, and the lambda_format gives callable functions. These use the variable names you have provided.

There are also some helper functions for doing this quickly. You can call get_hof() (or pass an equation file explicitly to this) to get this pandas dataframe.

You can call the functions best() to get the sympy format for the best equation, using the score column to sort equations. best_latex() returns the LaTeX form of this, and best_callable() returns a callable function.

`loss`

The default loss is mean-square error, and weighted mean-square error. One can pass an arbitrary Julia string to define a custom loss, using, e.g., loss="myloss(x, y) = abs(x - y)^1.5". For more details, see the Losses page for SymbolicRegression.jl.

Here are some additional examples:

abs(x-y) loss

pysr(..., loss="f(x, y) = abs(x - y)^1.5")

Note that the function name doesn't matter:

pysr(..., loss="loss(x, y) = abs(x * y)")

With weights:

pysr(..., weights=weights, loss="myloss(x, y, w) = w * abs(x - y)")

Weights can be used in arbitrary ways:

pysr(..., weights=weights, loss="myloss(x, y, w) = abs(x - y)^2/w^2")

Built-in loss (faster) (see losses). This one computes the L3 norm:

pysr(..., loss="LPDistLoss{3}()")

Can also uses these losses for weighted (weighted-average):

pysr(..., weights=weights, loss="LPDistLoss{3}()")