Parameter vs Hyperparameters In Machine Learning
Parameters are the values that are learned by a model during training, whereas hyperparameters are those that are set before the model is trained.
During training, the parameters of a model are determined by the data. These values are used to make predictions based on new data. Parameters include the weights of a neural network and the coefficients of a linear regression model.
Hyperparameters, on the other hand, are values that are set prior to training. These values determine the learning algorithm and model. An example of a hyperparameter is the learning rate, the number of hidden layers, and the strength of regularization of a neural network.
In order to optimize the performance of a model, parameters and hyperparameters must be set correctly. The process of tuning hyperparameters involves finding the best parameters for a given problem, whereas training involves learning these parameters.
The following approaches can be used to perform hyperparameter search:
1. Grid Search
1.For grid search, a set of possible hyperparameter values is specified, and then a model is trained and evaluated for each combination of hyperparameter values. It is a simple method to implement, but it can be computationally expensive when dealing with high-dimensional hyperparameter spaces.
2.For example, if a model has two hyperparameters, say “learning rate” and “number of hidden layers” and we want to test the model with learning rate = [0.01, 0.001, 0.0001], and number of hidden layers = [1, 2, 3] then grid search would train the model for all the combination of the hyperparameters.
3. The process can be summarized as
1.Define a set of possible values for each hyperparameter
2.Create a grid of all possible combinations of the hyperparameter values
3.Train and evaluate a model for each combination of hyperparameter values
4.Select the combination of hyperparameter values that results in the best performance on the validation set.
4. The main advantage of grid search is that it is simple to implement and understand. However, it can be computationally expensive, especially when dealing with a large number of hyperparameters or a large search space. Therefore, it is often used in combination with other techniques such as random search or Bayesian optimization, to more efficiently explore the search space.
2. Random Search
1.This method involves randomly sampling hyperparameter values from a predefined distribution and then training and evaluating a model using each set of samples. In the case of high-dimensional hyperparameter spaces, this approach can be more efficient than grid search due to its reduced computational cost.
2.Random search involves creating a set of candidate solutions, known as “points” or “vectors”, within a search space. As a result of the analysis, each point is assigned a scalar value that represents its quality or “fitness”, known as the “objective function” or “fitness function”. The optimization process aims to find the best or near-optimal solution by finding the point with the highest fitness.
3.It depends on the complexity of the problem and the desired level of accuracy of the solution how many points are generated and how large the search space is. There is a higher chance of finding a good solution if more points are generated and evaluated. This increases the computational cost of the optimization process, however. For balancing the trade-off between accuracy and computational cost, practitioners often perform random searches for a fixed number of iterations or until a certain stopping criterion has been achieved to allow for a good trade-off between accuracy and computational cost.
4.The simplicity of random search is one of the main advantages of this method. In addition, it does not make any assumptions about the structure of the search space nor does it require any gradient information. It is also easy to parallelize and can be used in conjunction with other optimization methods to achieve the best results. The main disadvantage of random search, however, is that it is relatively less efficient than other optimization methods, such as gradient descent or evolutionary algorithms, as compared to other optimization methods. Because random search does not take into account any of the structure of the search space or the previous evaluations, it can be less efficient in finding good solutions since it does not consider the structure of the search space.
5.As a final point, I would like to emphasize that random search is a simple, efficient, and easy method of optimizing large and complex search spaces. With it, you can find a near-optimal solution with as few evaluations as possible, so you can speed up the optimization process by finding a good solution with as few evaluations as possible. Neither gradient information nor assumptions about the structure of the search space are required in order to carry out this search. In spite of the fact that it does not take into account the structure of the search space or the previous evaluations, its effectiveness is fairly low compared to other optimization methods.
3. Bayesian optimization
1.Bayesian optimization determines which point in the search space to sample next according to a probabilistic model of the underlying objective function. If the objective function is expensive to evaluate, this approach may be more efficient than grid search or random search.
2.A Bayesian optimization method involves modelling a function that is unknown as a probability distribution, called a surrogate function or acquisition function, that expresses the current belief about the behavior of the function. In order to make better decisions about the next point to evaluate, the model is updated after each function evaluation.
3.An optimization process begins with a small number of initial evaluations of the function, typically obtained by randomly sampling the search space. Probabilistic models such as Gaussian processes are fitted to the function based on these evaluations. In addition to predicting the function’s behavior, the model can also estimate the degree of uncertainty it is subject to.
4.Next, an acquisition function is used to determine the next point to evaluate, which is a trade-off between exploration and exploitation. It balances exploring new regions of the search space where the function may have a high value with exploiting the current best point. Probability of Improvement (PI), Expected Improvement (EI), and Upper Confidence Bound (UCB) are popular acquisition functions.
5.Other optimization methods cannot compare with Bayesian optimization. Due to its small number of function evaluations, it is efficient when dealing with expensive black-box functions. In addition, it can handle complex search spaces and noisy functions. Furthermore, it provides a measure of uncertainty for the predicted function value anywhere in the search space, which can be helpful in making decisions.
6.However, Bayesian optimization also has some limitations. It can be sensitive to the choice of the probabilistic model, the acquisition function, and the initialization of the optimization process. Additionally, it can be computationally expensive for high-dimensional search spaces and can require a lot of memory to store the model.
7. The Bayesian optimization method is a global optimization method for black-box functions that can be expensive to evaluate and do not have a closed-form expression. A probability distribution is modeled to represent the unknown function, updated after each evaluation, and an acquisition function is maximized to select the next point to evaluate. A probabilistic model, acquisition function, and the initialization of the optimization process play a key role in its efficiency and ability to handle noisy functions and high-dimensional search spaces.
4. Gradient-based Optimization
1.Gradient-based optimization involves iteratively updating the hyperparameters using the gradient information of the objective function. When the function is differentiable, this method is applicable, and it is commonly used in deep learning applications.
2.The basic idea behind gradient-based optimization is to iteratively move in the direction of the negative gradient of the function to be optimized. The gradient is a vector that points in the direction of the steepest increase of the function. By taking small steps in the direction of the negative gradient, the algorithm approaches the minimum of the function
3.The most commonly used algorithm that uses gradient-based optimization is gradient descent. In gradient descent, the parameters of the model are initialized randomly and then updated at each iteration according to the following rule:
Parameters = parameters — learning_rate * gradient
4. The learning rate is a hyperparameter that controls the size of the steps taken in the direction of the negative gradient. A smaller learning rate will take smaller steps and converge more slowly, while a larger learning rate will take larger steps and converge more quickly, but may overshoot the minimum.
5. In summary, gradient-based optimization is a method of iteratively moving in the direction of the negative gradient of a function to find its minimum or maximum. It is an important technique used in many machine learning and deep learning algorithms to optimize model parameters and minimize the error or loss function.
Python Library for Hyperparameter Optimization
1.Scikit-learn’s GridSearchCV and RandomizedSearchCV:
A grid search and a random search for hyperparameters can be done quickly and easily using these libraries. They can be used with any scikit-learn estimator and provide an efficient and simple method of optimizing hyperparameters
2. Keras Tuner:
This library is designed specifically for Keras and TensorFlow, and allows you to tune deep learning models’ hyperparameters. A variety of built-in tuners are available, including random search, grid search, and Bayesian optimization.
3. Optuna:
In this library, you will find a lightweight, yet powerful Python library for optimizing hyperparameters. Both researchers and practitioners can use it easily and efficiently, and parallelization, pruning, and resuming trials are supported.
4. Hyperopt:
Optimizing complex and large-scale problems is made easy and flexible with this library. A tree of Parzen estimators is used to model the unknown objective function, and several optimization algorithms are provided, including TPE (Tree-structured Parzen Estimator) and Random Search.
5. Spearmint:
Bayesian optimization can be performed using this Python library. The application provides several acquisition functions, including expected improvement and probability of improvement, using the GPy library for Gaussian Processes.
6. Skopt:
Using this library, Bayesian optimization can be performed simply and efficiently. With its tree-based optimization and randomized optimization algorithms, it is built on top of the scikit-learn library.
7.Bayesian Optimization:
Bayesian optimization is implemented in pure Python with this library. By using it, you can optimize expensive black-box functions in a simple and efficient manner.
8. Hyperband:
A simple and efficient library for performing hyperband optimization is provided by this library. For both researchers and practitioners, it is designed to be easy to use and efficient.
9. Optimal:
Using this library, you can perform optimizations in a simple and efficient manner. Gradient descent, conjugate gradients, and Newton’s method are among the optimization algorithms included in the program.
References
1.Source: ChatGPT
2.https://towardsdatascience.com/hyperparameters-optimization-526348bb8e2d
