code: def regression(
      target,
      predictions,
      sensitive_features,
      fairness_metric,
      fairness_threshold,
      privileged_groups=[],
      underprivileged_groups=[],
      previous_fairness_optimization=None,
      performance_metric=None,
      performance_metric_name=None,
  ):
      target = np.array(target).ravel()
      preds = np.array(predictions)
  
      # fairness optimization stats
      sensitive_values = {}
      for col in sensitive_features.columns:
          col_name = col[10:]  # skip 'senstive_'
          values = list(sensitive_features[col].unique())
          sensitive_values[col] = values
  
          for v in values:
              ii = sensitive_features[col] == v
  
          new_sensitive_values = {}
          for k, prev_values in sensitive_values.items():
              if k == col:
                  continue
              new_sensitive_values[f"{k}@{col}"] = []
              for v in values:
                  for pv in prev_values:
                      if isinstance(pv, tuple):
                          new_sensitive_values[f"{k}@{col}"] += [
                              (*pv, v)
                          ]
                      else:
                          new_sensitive_values[f"{k}@{col}"] += [
                              (pv, v)
                          ]
  
          sensitive_values = {
              **sensitive_values,
              **new_sensitive_values,
          }
  
      sensitive_indices = {}
      least_frequent_key = None
      least_frequency = sensitive_features.shape[0]
      for k, values_list in sensitive_values.items():
          if k.count("@") == sensitive_features.shape[1] - 1:
              # print(k)
              # print("values_list",values_list)
              cols = k.split("@")
              for values in values_list:
                  if not isinstance(values, tuple):
                      values = (values,)
                  # print("values", values)
  
                  ii = None
                  for i, c in enumerate(cols):
                      if ii is None:
                          ii = sensitive_features[c] == values[i]
                      else:
                          ii &= sensitive_features[c] == values[i]
  
                  key = "@".join([str(s) for s in values])
                  if np.sum(ii) > 0:
                      sensitive_indices[key] = ii
                      if np.sum(ii) < least_frequency:
                          least_frequency = np.sum(ii)
                          least_frequent_key = key
  
      weights = {}
      performance = {}
  
      for key, indices in sensitive_indices.items():
          w = target.shape[0] / len(sensitive_indices) / np.sum(indices)
          weights[key] = w
          performance[key] = performance_metric(
              target[indices], predictions[indices]
          )
  
      # try to upscale more the largest weight
      weights[least_frequent_key] *= 1.5
  
      denominator = np.max(list(performance.values()))
      new_performance = {}
      for k, v in performance.items():
          new_performance[k] = np.round(v / denominator, 4)
      performance = new_performance
  
      previous_weights = {}
      if previous_fairness_optimization is not None:
          weights = previous_fairness_optimization.get("weights")
          for key, indices in sensitive_indices.items():
              direction = 0.0
              if (
                  previous_fairness_optimization["performance"][key]
                  < performance[key]
              ):
                  direction = 1.0
              elif performance[key] > fairness_threshold:
                  direction = 0.0
              else:
                  direction = -0.5
  
              # need to add previous weights instead 1.0
              prev_weights = previous_fairness_optimization.get(
                  "previous_weights", {}
              ).get(key, 1)
              delta0 = weights[key] - prev_weights
              previous_weights[key] = weights[key]
              weights[key] = max(
                  weights[key] + direction * delta0, 0.01
              )
  
      no_weights_change = False
      if str(previous_weights) == str(weights):
          no_weights_change = True
  
      step = None
      if previous_fairness_optimization is not None:
          step = previous_fairness_optimization.get("step")
  
      if step is None:
          step = 0
      else:
          if not no_weights_change:
              step += 1
  
      return {
          "performance": performance,
          "previous_weights": previous_weights,
          "weights": weights,
          "step": step,
          "fairness_threshold": fairness_threshold,
      }
  
imports: import os
  import numpy
  import pandas
  from matplotlib import pyplot
label_desc: Use image node_id 2 for calling the FairnessOptimization obj's underlying member method code with example usage: obj.regression(target, predictions, sensitive_features, fairness_metric, fairness_threshold, privileged_groups, underprivileged_groups, previous_fairness_optimization, performance_metric, performance_metric_name) and returns: dict