 # Optimization Techniques In Data Science

2022-08-12 by Anusha A

Data science is a relatively new field that focuses on analyzing large amounts of data via various methods to make the data more intelligible. To comprehend the field of data science, we will need a solid foundation in the following three areas of knowledge: statistics, linear algebra, and optimization.

However, in today's article, we will understand Optimization and its various techniques in data science. Let's get started and before we jump directly to the techniques, let us understand what optimization is.

## Optimization: Brief Introduction

The term "optimization" refers to a process or method utilized to determine the most effective solution. The requirement will determine whether its value is the minimum or the maximum for that category. For instance, if a company is required to find a means to make a maximum return on their products, then the condition will be maximum. On the other hand, if the company wants to discover a technique by which their business earns the least product cost on production, then the need will be minimal.

## Various Optimization Techniques in Data Science

Let us now look into the various optimization techniques in data science. Here they are:

The gradient descent approach is currently the method of choice for optimization. The objective of this tactic is to update the variables iteratively in a way that is opposed to how the gradients of the objective function move. This strategy directs the model to discover the target with each update, eventually converging to the optimal value for the objective function.

2. Stochastic Gradient Descent

The stochastic gradient descent (SGD) algorithm was developed to solve the high computing cost involved in each iteration of the process when dealing with enormous amounts of data. The equation can be written as follows:

Back-propagation refers to taking the values and iteratively modifying them depending on various parameters to lower the loss function.

Instead of directly calculating the exact value of the gradient, this approach updates the gradient (theta) by randomly using one sample at each iteration. This is done in place of directly calculating the gradient's value. The stochastic gradient approximates the true gradient that does not consider any outside factors. This optimization approach cuts down on the amount of time needed to do an update when working with a large number of samples, and it also eliminates some redundant computational work.

3. The Technique of Adaptive Learning Rate

Learning rate is one of the primary hyperparameters optimized during the process. The model's behavior depends on the learning rate, which determines whether it will pass over particular data sections. When the learning rate is high, there is a possibility that the model will overlook more nuanced parts of the data. If it is low, then it is preferable for applications that take place in the real world. The rate of learning has a significant impact on the Stochastic Gradient Descent (SGD). It can be difficult to determine what the optimal value of the learning rate should be. It was suggested that adaptive approaches could automatically do this tweaking.

In Deep Neural Networks (DNNs), the adaptive forms of SGD have seen the widespread application. Methods such as AdaDelta, RMSProp, and Adam all use exponential averaging to offer accurate updates while keeping the process as straightforward as possible.

• Weights with a steep gradient will have a slow learning rate and vice versa. This is known as the degrade formula.
• RMSprop modifies the Adagrad method so that it slows the rate at which it monotonically decreases the amount learned.
• Adam is virtually identical to RMSProp, except that he possesses momentum.
• The Alternating Direction Method of Multipliers, sometimes known as ADMM, is an additional alternative to the Stochastic Gradient Descent method (SGD)

The learning rate is not predetermined in either the gradient descent or AdaGrad approaches, which is the key distinction between the two. The computation for it makes use of all of the historical gradients that have been accumulated up to the most recent iteration.

4. Method of the Conjugate Gradient

The conjugate gradient (CG) method is applied in the process of solving nonlinear optimization issues in addition to large-scale linear systems of equations. A slow convergence speed is characteristic of first-order approaches. On the other hand, the approaches of the second order require a lot of resources. An intermediate algorithm known as conjugate gradient optimization combines the benefits of first-order information with the high-order methods' ability to ensure rapid convergence.

5. Optimization Without the Use of Derivatives

Certain optimization problems are almost always solvable by employing a gradient, notwithstanding the possibility that the derivative of the objective function does not exist or is difficult to calculate. This is due to the fundamental characteristics of the issue. Derivative-free optimization enters the picture at this point to help solve the problem. Instead of deriving solutions methodically, it uses a heuristic algorithm that picks approaches that have previously been successful. There are numerous examples of this: genetic algorithms, particle swarm optimization, and classical simulated annealing arithmetic.

6. Zeroth Order Optimisation

Recent years have seen the development of derivative-free optimization's successor, zeroth order optimization, which aims to remedy the faults of its predecessor. Methods of optimization that don't use derivatives have trouble scaling up to huge problems and don't provide a way to analyze how quickly they converge on a solution.

Advantages of the Zeroth Order include the following:

• Ease of implementation that requires only a minor adjustment to the gradient-based methods that are most frequently employed
• Approximations of derivatives that are computationally efficient in situations when the derivatives themselves are difficult to compute
• convergent rates that are comparable to those of first-order algorithms.

## Final Words

With this, we come to an end for today's article. To summarize what we learned, first, we understood optimization in brief and its essence. Then, we understood the different optimization techniques in data science, including Gradient Descent, Stochastic Gradient Descent, Method of Adaptive Learning, and the rest.

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