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Brock & Hommes¤

BrockHommes ¤

Bases: Model

Differentiable implementation of the Brock and Hommes (1998) model. See equations (39) and (40) of https://arxiv.org/pdf/2202.00625.pdf for reference.

Arguments:

  • n_timesteps: Number of timesteps to simulate. Default: 100.
Source code in blackbirds/models/brock_hommes.py 
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class BrockHommes(Model):
    r"""Differentiable implementation of the Brock and Hommes (1998) model. See equations (39) and (40)
    of https://arxiv.org/pdf/2202.00625.pdf for reference.

    **Arguments:**

    - `n_timesteps`: Number of timesteps to simulate. Default: 100.
    """

    def __init__(self, n_timesteps=100, device="cpu"):
        super().__init__()
        self.n_timesteps = n_timesteps
        self._eps = torch.distributions.normal.Normal(
            torch.tensor([0.0], device=device), torch.tensor([1.0], device=device)
        )
        self.device = device

    def initialize(self, params):
        return torch.zeros((3, 1))

    def trim_time_series(self, x):
        return x[-3:]

    def step(self, params, x):
        r"""
        Runs the model forward for one time-step. Parameters follow the order: log_beta, g1, g2, g3, g4, b1, b2, b3, b4, log_sigma, log_r

        **Arguments:**

        - `params`: A list of parameters. Parameters follow the order: log_beta, g1, g2, g3, g4, b1, b2, b3, b4, log_sigma, log_r
        - `x`: The current state of the model.

        !!! danger
            beta, sigma, and r are given in log.
        """
        beta = torch.exp(params[0])
        g = params[1:5]
        b = params[5:9]
        sigma = torch.exp(params[-2])
        r = torch.exp(params[-1])
        R = 1.0 + r
        g = soft_maximum(soft_minimum(g, torch.tensor(1.0), 2), torch.tensor(1e-3), 2)

        epsilon = self._eps.rsample()
        exponent = beta * (x[-1] - R * x[-2]) * (g * x[-3] + b - R * x[-2])
        norm_exponentiated = torch.nn.Softmax(dim=-1)(exponent)
        mean = (norm_exponentiated * (g * x[-1] + b)).sum()
        x_t = (mean + epsilon * sigma) / R
        return x_t.reshape(1, -1)

    def observe(self, x):
        return [x.flatten()]

step(params, x) ¤

Runs the model forward for one time-step. Parameters follow the order: log_beta, g1, g2, g3, g4, b1, b2, b3, b4, log_sigma, log_r

Arguments:

  • params: A list of parameters. Parameters follow the order: log_beta, g1, g2, g3, g4, b1, b2, b3, b4, log_sigma, log_r
  • x: The current state of the model.

Danger

beta, sigma, and r are given in log.

Source code in blackbirds/models/brock_hommes.py 
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def step(self, params, x):
    r"""
    Runs the model forward for one time-step. Parameters follow the order: log_beta, g1, g2, g3, g4, b1, b2, b3, b4, log_sigma, log_r

    **Arguments:**

    - `params`: A list of parameters. Parameters follow the order: log_beta, g1, g2, g3, g4, b1, b2, b3, b4, log_sigma, log_r
    - `x`: The current state of the model.

    !!! danger
        beta, sigma, and r are given in log.
    """
    beta = torch.exp(params[0])
    g = params[1:5]
    b = params[5:9]
    sigma = torch.exp(params[-2])
    r = torch.exp(params[-1])
    R = 1.0 + r
    g = soft_maximum(soft_minimum(g, torch.tensor(1.0), 2), torch.tensor(1e-3), 2)

    epsilon = self._eps.rsample()
    exponent = beta * (x[-1] - R * x[-2]) * (g * x[-3] + b - R * x[-2])
    norm_exponentiated = torch.nn.Softmax(dim=-1)(exponent)
    mean = (norm_exponentiated * (g * x[-1] + b)).sum()
    x_t = (mean + epsilon * sigma) / R
    return x_t.reshape(1, -1)