Warning: Just in case the terms "partial derivative" or "gradient" sound unfamiliar, I suggest checking out these resources! Gradient descent is an iterative algorithm whose purpose is to make changes to a set of parameters (i.e. A loss or cost or objective function (any of these naming conventions work in practice) is the function whose value we seek to minimize. When performing Gradient descent, each time we update the parameters, we expect to observe a change in min f(w). That is at each iteration, the gradient of the function that contains parameters in w is taken so that changes in the function with respect to parameters brings us closer to the goal of reaching an optimal set of parameters that will ultimately lead to the lowest possible loss function value.
To deal with the complexity of the new bigger and more complex generation of data, machine learning (ML) techniques are probably the first and foremost used. For ML algorithms to produce results in a reasonable amount of time, they need to be implemented efficiently. In this paper, we analyze one of the means to increase the performances of machine learning algorithms which is exploiting data locality. Data locality and access patterns are often at the heart of performance issues in computing systems due to the use of certain hardware techniques to improve performance. Altering the access patterns to increase locality can dramatically increase performance of a given algorithm. Besides, repeated data access can be seen as redundancy in data movement. Similarly, there can also be redundancy in the repetition of calculations. This work also identifies some of the opportunities for avoiding these redundancies by directly reusing computation results. We start by motivating why and how a more efficient implementation can be achieved by exploiting reuse in the memory hierarchy of modern instruction set processors. Next we document the possibilities of such reuse in some selected machine learning algorithms. Keywords: Increasing data locality, data redundancy and reuse, machine learning, supervised learners... Notice This an extended version of the paper titled "Reviewing Data Access Patterns and Computational Redundancy for Machine Learning Algorithms" that appeared in the proceedings of the IADIS International Conference Big Data Analytics, Data Mining and Computational Intelligence 2019 (part of MCCSIS 2019)"  The final publication of this article is available at IOS Press through http://dx.doi.org/10.3233/IDA-184287. Because processor speed is increasing at a much faster rate than memory speed, computer architects have turned increasingly to the use of memory hierarchies with one or more levels of cache memory. This caching technique takes advantage of data locality in programs which is the property that references to the same memory location (temporal locality) or adjacent locations (spatial locality) reused within a short period of time. 1 One of the most popular ways to increase it is to rewrite the data intensive parts of the program, almost always the loops . A simple example of this is to interchange the two loops in Algorithm 1 such that the code looks like Algorithm 2; note that the indices in the loop headers have changed.
We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation operations per iteration, which has a computational cost comparable to two standard forward passes and is easy to implement. Our method addresses long-standing issues with current second-order solvers, which invert an approximate Hessian matrix every iteration exactly or by conjugate-gradient methods, a procedure that is both costly and sensitive to noise. Instead, we propose to keep a single estimate of the gradient projected by the inverse Hessian matrix, and update it once per iteration. This estimate has the same size and is similar to the momentum variable that is commonly used in SGD. No estimate of the Hessian is maintained. We first validate our method, called CurveBall, on small problems with known closed-form solutions (noisy Rosenbrock function and degenerate 2-layer linear networks), where current deep learning solvers seem to struggle. We then train several large models on CIFAR and ImageNet, including ResNet and VGG-f networks, where we demonstrate faster convergence with no hyperparameter tuning. Code is available.
In this article, we will discuss regularization and optimization techniques that are used by programmers to build a more robust and generalized neural network. We will study the most effective regularization techniques like L1, L2, Early Stopping, and Drop out which help for model generalization. We will take a deeper look at different optimization techniques like Batch Gradient Descent, Stochastic Gradient Descent, AdaGrad, and AdaDelta for better convergence of the neural networks. Overfitting and underfitting are the most common problems that programmers face while working with deep learning models. A model that is well generalized to data is considered to be an optimal fit for the data.
The term "optimization" refers to the process of iteratively training a model to produce a maximum and minimum function evaluation to get a minimum cost function. It is crucial since it will assist us in obtaining a model with the least amount of error (as there will be discrepancies between the actual and predicted values). There are various optimization methods; in this article, we'll look at gradient descent and its three forms: batch, stochastic, and mini-batch. Note: Hyperparameter optimization is required to fine-tune the model. Before you begin training the model, you must first specify hyperparameters.