|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/sts/forecast.py#L410-L546) | Runs posterior inference to impute the missing values in a time series. (deprecated argument values) tfp.sts.impute_missing_values( model, observed_time_series, parameter_samples, include_observation_noise=False, timesteps_are_event_shape=True ) > [!WARNING] > **Deprecated:** SOME ARGUMENT VALUES ARE DEPRECATED: `(timesteps_are_event_shape=True)`. They will be removed after 2021-12-31. Instructions for updating: `Imputed distributions returned by`tfp.sts.impute_missing_values`will soon compute per-timestep probabilities (treating timesteps as part of the batch shape) instead of a single probability for an entire series (the current approach, in which timesteps are treated as event shape). Please update your code to pass`timesteps_are_event_shape=False\` (this will soon be the default) and to explicitly sum over the per-timestep log probabilities if this is required. This method computes the posterior marginals `p(latent state | observations)`, given the time series at observed timesteps (a missingness mask should be specified using [`tfp.sts.MaskedTimeSeries`](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/MaskedTimeSeries)). It pushes this posterior back through the observation model to impute a predictive distribution on the observed time series. At unobserved steps, this is an imputed value; at other steps it is interpreted as the model's estimate of the underlying noise-free series.


| ## Args || |---|---| | `model` | [`tfp.sts.Sum`](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/Sum) instance defining an additive STS model. | | `observed_time_series` | `float` `Tensor` of shape `concat([sample_shape, model.batch_shape, [num_timesteps, 1]])` where `sample_shape` corresponds to i.i.d. observations, and the trailing `[1]` dimension may (optionally) be omitted if `num_timesteps > 1`. Any `NaN`s are interpreted as missing observations; missingness may be also be explicitly specified by passing a [`tfp.sts.MaskedTimeSeries`](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/MaskedTimeSeries) instance. | | `parameter_samples` | Python `list` of `Tensors` representing posterior samples of model parameters, with shapes `[concat([ [num_posterior_draws], param.prior.batch_shape, param.prior.event_shape]) for param in model.parameters]`. This may optionally also be a map (Python `dict`) of parameter names to `Tensor` values. | | `include_observation_noise` | If `False`, the imputed uncertainties represent the model's estimate of the noise-free time series at each timestep. If `True`, they represent the model's estimate of the range of values that could be *observed* at each timestep, including any i.i.d. observation noise. Default value: `False`. | | `timesteps_are_event_shape` | Deprecated, for backwards compatibility only. If `False`, the predictive distribution will return per-timestep probabilities Default value: `True`. |



| ## Returns || |---|---| | `imputed_series_dist` | a `tfd.MixtureSameFamily` instance with event shape `[num_timesteps] if timesteps_are_event_shape else []` and batch shape `concat([sample_shape, model.batch_shape, [] if timesteps_are_event_shape else [num_timesteps])`, with `num_posterior_draws` mixture components. |
#### Example To specify a time series with missing values, use [`tfp.sts.MaskedTimeSeries`](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/MaskedTimeSeries): time_series_with_nans = [-1., 1., np.nan, 2.4, np.nan, 5] observed_time_series = tfp.sts.MaskedTimeSeries( time_series=time_series_with_nans, is_missing=tf.math.is_nan(time_series_with_nans)) Masked time series can be passed to [`tfp.sts`](https://www.tensorflow.org/probability/api_docs/python/tfp/sts) methods in place of a `observed_time_series` `Tensor`: # Build model using observed time series to set heuristic priors. linear_trend_model = tfp.sts.LocalLinearTrend( observed_time_series=observed_time_series) model = tfp.sts.Sum([linear_trend_model], observed_time_series=observed_time_series) # Fit model to data parameter_samples, _ = tfp.sts.fit_with_hmc(model, observed_time_series) After fitting a model, `impute_missing_values` will return a distribution # Impute missing values imputed_series_distribution = tfp.sts.impute_missing_values( model, observed_time_series, parameter_samples=parameter_samples) print('imputed means and stddevs: ', imputed_series_distribution.mean(), imputed_series_distribution.stddev())