Bagging Aggregation

mediumFREEEnsemble MethodsMachine Learning 1

Implement bagging aggregation for an ensemble of model predictions.

Given predictions from $m$ models for $n$ data points:

For classification (mode="classify"): return the majority vote for each data point
For regression (mode="regress"): return the mean prediction for each data point

In case of a tie in majority voting, return the smallest class label.

Return a list of aggregated predictions, rounded to 4 decimal places for regression.

Example

Input

predictions = [[1, 0, 1], [0, 0, 1], [1, 1, 1]]
mode = "classify"

Output

[1, 0, 1]

Reasoning

predictions holds one row per model and one column per data point. Here $m = 3$ models each label $n = 3$ points, so the answer has 3 entries, one per column. mode is "classify", so each column is decided by majority vote.
Point 1 (first column): the three models say $1, 0, 1$ . Label $1$ gets 2 votes, label $0$ gets 1, so the vote is $1$ .
Point 2: the models say $0, 0, 1$ . Label $0$ wins $2$ to $1$ , so the vote is $0$ .
Point 3: all three say $1$ , a unanimous $3$ to $0$ , so the vote is $1$ .
Reading the winners across the columns gives [1, 0, 1]. Notice that point 1 is not a tie: a tie needs two labels with the same top count, e.g. $0, 1$ from two models, and then the smaller label $0$ wins.
In regression mode the column is averaged instead: models predicting $2.0, 4.0, 3.0$ give $\frac{9}{3} = 3.0$ , rounded to 4 decimal places.

Constraints

predictions: 2D list (m models x n data points)
mode: "classify" or "regress"
Return list of n aggregated predictions
For regression, round to 4 decimal places
For ties in classification, use the smallest label

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Concept primer

Background Knowledge

Ensemble Methods are a class of machine learning techniques that combine the predictions of multiple models to produce a single, more accurate prediction. Bagging aggregation is a type of ensemble method that involves training multiple models on different subsets of the training data and then combining their predictions. This approach can help to reduce overfitting and improve the overall performance of the model.

In the context of bagging aggregation, each model is trained on a bootstrap sample of the training data, which is a random subset of the data with replacement. This means that some data points may be included multiple times in the sample, while others may be excluded. By training multiple models on different bootstrap samples, we can capture different aspects of the data and reduce the impact of noise and outliers. The predictions of the individual models are then combined using a voting scheme, such as majority voting for classification or mean prediction for regression.

The key benefits of bagging aggregation are its ability to reduce variance and improve robustness. By combining the predictions of multiple models, we can reduce the impact of overfitting and produce a more stable and accurate prediction. Additionally, bagging aggregation can be used with any type of model, including decision trees, neural networks, and linear models. This makes it a versatile and widely applicable technique in machine learning.

Algorithm/Approach

The general approach to solving this problem involves implementing a bagging aggregation algorithm that combines the predictions of multiple models. The algorithm should take the predictions of the individual models as input and produce a single, aggregated prediction as output. The approach will depend on the specific mode of the problem, either classification or regression. For classification, the algorithm will use a majority voting scheme to determine the most popular class label. For regression, the algorithm will use a mean prediction scheme to determine the average predicted value.

Step-by-Step Strategy

To implement the solution, follow these steps:

Determine the mode of the problem, either classification or regression.
For classification, implement a majority voting scheme to determine the most popular class label for each data point. In case of a tie, return the smallest class label.
For regression, implement a mean prediction scheme to determine the average predicted value for each data point.
Round the aggregated predictions to 4 decimal places for regression.
Return a list of aggregated predictions.

Common Pitfalls

Some common pitfalls to watch out for when implementing bagging aggregation include:

Failing to handle ties in majority voting for classification.
Failing to round the aggregated predictions to 4 decimal places for regression.
Using the wrong voting scheme for the specific mode of the problem.
Failing to consider the impact of noise and outliers on the predictions of the individual models.

Time & Space Complexity

The time complexity of the bagging aggregation algorithm will depend on the number of models and the number of data points. In general, the time complexity will be O(nm), where n is the number of data points and m is the number of models. The space complexity will also depend on the number of models and the number of data points, and will be O(nm) in the worst case. However, the actual time and space complexity may be less depending on the specific implementation and the characteristics of the data.

solution.py

Python 3.13

Test results