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A non-parametric learning algorithm is a machine learning approach that doesn't make strong assumptions about the functional form of the underlying data distribution or the number of parameters needed to represent it. In contrast to parametric models, which assume a fixed number of parameters to describe the data, non-parametric models can flexibly adapt to the complexity of the data without predefining the model's structure.

Some key characteristics of non-parametric learning algorithms include:

1. Flexibility: Non-parametric models can capture complex relationships in the data without requiring a specific functional form to be specified in advance. They are often well-suited for tasks where the underlying data distribution is not well-known or may be highly variable. In non-parametric algorithms, the amount of data and parameters (θ_i), you need, keep growth with the size of the data.

2. Scalability: Non-parametric models can handle data of varying sizes and dimensions without the need to adjust the model's structure. This scalability makes them useful for both small and large datasets.

3. Memory-Intensive: Non-parametric models typically require more memory because they often store information about the entire dataset or a substantial subset of it. This can be a limitation when working with very large datasets.

4. Adaptability: Non-parametric models can adapt to the complexity of the data as more data points become available, making them useful for tasks with changing or evolving data distributions.

Some common examples of non-parametric learning algorithms include:

1. K-Nearest Neighbors (K-NN): In K-NN, predictions are made by finding the K nearest data points to a given query point and taking a majority vote or weighted average of their labels.

2. Kernel Density Estimation (KDE): KDE estimates the probability density function of a continuous random variable by placing a kernel (smooth function) at each data point and summing them to create a smooth estimate.

3. Decision Trees (when used without pre-pruning): Decision trees can be considered non-parametric when they are allowed to grow deep and complex, adapting their structure to the data. However, they can also be made parametric by limiting their depth.

4. Random Forests and Gradient Boosted Trees: While individual decision trees can be non-parametric, ensembles like random forests and gradient boosted trees combine multiple trees to create more stable and powerful models.

5. Gaussian Processes: These are a non-parametric approach to regression and classification that model the underlying data distribution as a Gaussian process, allowing for flexible predictions and uncertainty estimation.

Non-parametric models can be powerful tools for certain types of data and applications, especially when dealing with complex, high-dimensional, or noisy datasets where parametric assumptions may not hold. However, they can also be computationally expensive and may require careful tuning to perform well.

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