python statsmodels：具有矩阵参数的自定义状态空间

如何解决python statsmodels：具有矩阵参数的自定义状态空间

我需要拟合如下状态空间模型：

y_t = Z\alpha_t + d + \epsilon_t; \quad \epsilon_t ~ N(0,diag(\sigma^2_\epsilon))

\alpha_{t+1} = T \alpha_t + \eta_t; \eta ~ N(0,I)

使用 y_t 一个 d 维向量（在我的例子中为 d~100）和 \alpha_t k维。

即“简单”线性状态空间模型，具有时间不变矩阵和对角噪声观测协方差。 如果不是对角协方差，pykalman 就可以完成这项工作。但是，据我所知，它不允许将观测协方差约束为对角线（您可以完全修复它，也可以在没有约束的情况下对其进行估计）。

因此，我转向 statsmodels 并尝试自定义 sm.tsa.statespace.MLEModel，但我不知道如何继续。我能找到的所有示例都导致要估计的标量参数很少，并且它们是通过 param_names 方法显式声明的，但我不知道如何处理矩阵参数。

我正在做这样的事情：

class myStateSpace(MLEModel):
    """
    linear state space with diagonal observation covariance
    """

    def __init__(self,endog,k_states):

        # initialize state space model
        super().__init__(endog=endog,k_states=k_states,k_posdef=k_states,initialization='approximate_diffuse',loglikelihood_burn=2)

        self.ssm["state_intercept"] = np.zeros(self.k_states)
        self.ssm["state_cov"] = np.eye(self.k_states)
        self.ssm["selection"] = np.eye(self.k_states)
        # remain to be optimized:
        # design,obs_intercept,transition,and diag components of obs_cov 

        # tell the model that obs_cov will be diag
        self._obs_cov_idx = ("obs_cov",) + np.diag_indices(self.k_endog)
        self._design_idx = ("design",) + np.indices((self.k_endog,self.k_states),sparse=True)
        self._transition_idx = ("transition",) + np.indices((self.k_states,sparse=True)
        self._obs_intercept_idx = ("obs_intercept",),sparse=True)


        # Which parameters need to be positive?
        # the last k_endog,namely the variances of obs_cov,# see param_names()
        self.num_params = self.k_states + self.k_states**2 + self.k_states*self.k_endog + self.k_endog 
        self.positive_parameters = np.array(range((self.num_params - self.k_endog),self.num_params))


    @property
    def param_names(self):
        design_names = ["design_%i%i" % (i,j) for i in range(self.K_endog) for j in range(self.k_states)]
        transition_names = ["transition_%i%i" % (i,j) for i in range(self.K_states) for j in range(self.k_states)]
        obs_intercept_names = ["state_intercept_%i" % i for i in range(self.k_endog)]
        obs_cov_names = ["obs_cov_%i" % i for i in range(self.K_endog)]

        return design_names + transition_names + obs_intercept_names + obs_cov_names 



    def transform_params(self,unconstrained):
            """
            constraint the variance parameters
            to be positive,"""
            constrained = unconstrained.copy()
            constrained[self.positive_parameters] = constrained[self.positive_parameters]**2
            return constrained

    def untransform_params(self,constrained):
            """
            Need to unstransform all the parameters you transformed
            in the `transform_params` function
            """
            unconstrained = constrained.copy()
            unconstrained[self.positive_parameters] = unconstrained[self.positive_parameters]**0.5
            return unconstrained

    def update(self,params,**kwargs):
        params = super().update(params,**kwargs)
        design_n = (self.k_states * self.k_endog)
        transition_n = design_n + self.k_states**2
        obs_intercept_n = transition_n + self.K_endog


        self.ssm[self._design_idx] = params[: design_n].reshape((self.k_endog,self.k_states))
        self[self._transition_idx] = params[design_n : transition_n].reshape((self.k_states,self.k_states))
        self[self._obs_intercept_idx] = params[transition_n : obs_intercept_n]
        self[self._obs_cov_idx] = params[-self.k_endog:]

除了还是怀念一个set_params方法之外，我觉得这种做法真的很牵强：有没有更直接的方式来处理矩阵参数而不用给每个参数起个名字？矩阵的入口？

此外，使用 self.ssm["transition"] 而不是 self["transition"]（我在示例中都见过）有什么区别？

感谢您的任何建议！