code: def predict(algo, pairs, *, n_jobs=None, **kwargs):
      """
      Generate predictions for user-item pairs.  The provided algorithm should be a
      :py:class:`algorithms.Predictor` or a function of two arguments: the user ID and
      a list of item IDs. It should return a dictionary or a :py:class:`pandas.Series`
      mapping item IDs to predictions.
  
      To use this function, provide a pre-fit algorithm::
  
          >>> from lenskit.algorithms.bias import Bias
          >>> from lenskit.metrics.predict import rmse
          >>> from lenskit import datasets
          >>> ratings = datasets.MovieLens('data/ml-latest-small').ratings
          >>> bias = Bias()
          >>> bias.fit(ratings[:-1000])
          <lenskit.algorithms.bias.Bias object at ...>
          >>> preds = predict(bias, ratings[-1000:])
          >>> preds.head()
                 user  item  rating   timestamp  prediction
          99004   664  8361     3.0  1393891425    3.288286
          99005   664  8528     3.5  1393891047    3.559119
          99006   664  8529     4.0  1393891173    3.573008
          99007   664  8636     4.0  1393891175    3.846268
          99008   664  8641     4.5  1393890852    3.710635
          >>> rmse(preds['prediction'], preds['rating'])
          0.8326992222...
  
      Args:
          algo(lenskit.algorithms.Predictor):
              A rating predictor function or algorithm.
          pairs(pandas.DataFrame):
              A data frame of (``user``, ``item``) pairs to predict for. If this frame also
              contains a ``rating`` column, it will be included in the result.
          n_jobs(int):
              The number of processes to use for parallel batch prediction.  Passed to
              :func:`lenskit.util.parallel.invoker`.
  
      Returns:
          pandas.DataFrame:
              a frame with columns ``user``, ``item``, and ``prediction`` containing
              the prediction results. If ``pairs`` contains a `rating` column, this
              result will also contain a `rating` column.
      """
      if n_jobs is None and "nprocs" in kwargs:
          n_jobs = kwargs["nprocs"]
          warnings.warn(
              "nprocs is deprecated, use n_jobs", DeprecationWarning
          )
  
      nusers = pairs["user"].nunique()
  
      timer = util.Stopwatch()
      with util.parallel.invoker(
          algo, _predict_user, n_jobs=n_jobs
      ) as worker:
          del algo  # maybe free some memory
  
          _logger.info(
              "generating %d predictions for %d users (setup took %s)",
              len(pairs),
              nusers,
              timer,
          )
          timer = util.Stopwatch()
          results = worker.map(
              (user, udf.copy())
              for (user, udf) in pairs.groupby("user")
          )
          results = pd.concat(results)
          _logger.info(
              "generated %d predictions for %d users in %s",
              len(pairs),
              nusers,
              timer,
          )
  
      if "rating" in pairs:
          return pairs.join(
              results.set_index(["user", "item"]), on=("user", "item")
          )
      return results
  
imports: import logging
  import warnings
  import pandas
  from ..None import util
label_desc: Use image node_id 2 for calling a global function with example usage: predict(algo, pairs) and returns: results, pairs