使用 pymc3 为具有多个似然函数的模型计算 WAIC

Calculating WAIC for models with multiple likelihood functions with pymc3

我尝试根据进球数预测足球比赛的结果,我使用以下模型:

with pm.Model() as model:
  # global model parameters
   h = pm.Normal('h', mu = mu, tau = tau)
   sd_a = pm.Gamma('sd_a', .1, .1) 
   sd_d = pm.Gamma('sd_d', .1, .1) 
   alpha = pm.Normal('alpha', mu=mu, tau = tau)

  # team-specific model parameters
   a_s = pm.Normal("a_s", mu=0, sd=sd_a, shape=n)
   d_s = pm.Normal("d_s", mu=0, sd=sd_d, shape=n)

   atts = pm.Deterministic('atts', a_s - tt.mean(a_s))
   defs = pm.Deterministic('defs', d_s - tt.mean(d_s))
   h_theta = tt.exp(alpha + h + atts[h_t] + defs[a_t])
   a_theta = tt.exp(alpha + atts[a_t] + defs[h_t])

  # likelihood of observed data
   h_goals = pm.Poisson('h_goals', mu=h_theta, observed=observed_h_goals)
   a_goals = pm.Poisson('a_goals', mu=a_theta, observed=observed_a_goals)

当我对模型进行采样时,迹线图看起来不错。

之后当我想计算 WAIC 时:

waic = pm.waic(trace, model)

我收到以下错误:


----> 1 waic = pm.waic(trace, model)

~\Anaconda3\envs\env\lib\site-packages\pymc3\stats_init_.py in wrapped(*args, **kwargs)
22 )
23 kwargs[new] = kwargs.pop(old)
—> 24 return func(*args, **kwargs)
25
26 return wrapped

~\Anaconda3\envs\env\lib\site-packages\arviz\stats\stats.py in waic(data, pointwise, scale)
1176 “”"
1177 inference_data = convert_to_inference_data(data)
-> 1178 log_likelihood = _get_log_likelihood(inference_data)
1179 scale = rcParams[“stats.ic_scale”] if scale is None else scale.lower()
1180

~\Anaconda3\envs\env\lib\site-packages\arviz\stats\stats_utils.py in get_log_likelihood(idata, var_name)
403 var_names.remove(“lp”)
404 if len(var_names) > 1:
–> 405 raise TypeError(
406 “Found several log likelihood arrays {}, var_name cannot be None”.format(var_names)
407 )

TypeError: Found several log likelihood arrays [‘h_goals’, ‘a_goals’], var_name cannot be None

当我在 pymc3 中有两个似然函数时,有什么方法可以计算 WAIC 和比较模型吗? (1: 主队进球数 2: 客队进球数)

这是可能的,但需要定义您有兴趣预测什么,它可以是比赛的结果,也可以是任何一支球队的进球数(不是总计,每场比赛将提供 2 个结果预测)。

PyMC discourse 提供了完整而详细的答案。

这里我把关注数量为匹配结果的情况记录下来作为总结。 ArviZ 将自动检索 2 个逐点对数似然数组,我们必须以某种方式组合它们(例如添加、连接、分组……)以获得单个数组。棘手的部分是知道哪个操作对应于每个数量,这必须在每个模型的基础上进行评估。在此特定示例中,可以通过以下方式计算匹配结果的预测准确性:

dims = {
    "home_points": ["match"],
    "away_points": ["match"],
}
idata = az.from_pymc3(trace, dims=dims, model=model)

设置 match 暗淡对于告诉 xarray 如何对齐逐点对数似然数组很重要,否则它们将不会以所需的方式广播和对齐。

idata.sample_stats["log_likelihood"] = (
    idata.log_likelihood.home_points + idata.log_likelihood.away_points
)
az.waic(idata)
# Output
# Computed from 3000 by 60 log-likelihood matrix
#
#           Estimate       SE
# elpd_waic  -551.28    37.96
# p_waic       46.16        -
#
# There has been a warning during the calculation. Please check the results.

注意 ArviZ>=0.7.0 是必需的。