# 확률적 경사 하강법

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## 노트

### 위키데이터

- ID : Q7617819

### 말뭉치

- The Stochastic Gradient Descent widget uses stochastic gradient descent that minimizes a chosen loss function with a linear function.
^{[1]} - We connected Stochastic Gradient Descent and Tree to Test & Score.
^{[1]} - We connect the File widget to Stochastic Gradient Descent, Linear Regression and kNN widget and all four to the Predictions widget.
^{[1]} - Stochastic Gradient Descent (SGD) addresses both of these issues by following the negative gradient of the objective after seeing only a single or a few training examples.
^{[2]} - Stochastic Gradient Descent (SGD) simply does away with the expectation in the update and computes the gradient of the parameters using only a single or a few training examples.
^{[2]} - Generally each parameter update in SGD is computed w.r.t a few training examples or a minibatch as opposed to a single example.
^{[2]} - In SGD the learning rate \alpha is typically much smaller than a corresponding learning rate in batch gradient descent because there is much more variance in the update.
^{[2]} - Implement the SGD, with a random initial condition \(x_0\).
^{[3]} - SGD is thus advantageous when \(n\) is very large, and one cannot afford to do several passes through the data.
^{[3]} - Implement the Stochastic gradient descent with averaging.
^{[3]} - Note that in contrast to SGD and SGA, this method uses a fixed step size \(\tau\).
^{[3]} - SGD often converges much faster compared to GD but the error function is not as well minimized as in the case of GD.
^{[4]} - Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited.
^{[5]} - In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better characterize the learning dynamics of SGD.
^{[5]} - Inspired from these work, we here analyze SGD from a geometrical perspective by inspecting the stochasticity of the norms and directions of minibatch gradients.
^{[5]} - So far we have played a bit fast and loose when it comes to talking about stochastic gradient descent.
^{[6]} - In particular, for a finite sample size we simply argued that the discrete distribution \(p(x, y) = \frac{1}{n} \sum_{i=1}^n \delta_{x_i}(x) \delta_{y_i}(y)\) allows us to perform SGD over it.
^{[6]} - Optimality guarantees for SGD are in general not available in nonconvex cases since the number of local minima that require checking might well be exponential.
^{[6]} - In a “purist” implementation of SGD, your mini-batch size would be set to 1.
^{[7]} - In order to apply Stochastic Gradient Descent, we need a dataset.
^{[7]} - In today’s blog post, we learned about Stochastic Gradient Descent (SGD), an extremely common extension to the vanilla gradient descent algorithm.
^{[7]} - SGD is also very common when training your own neural networks and deep learning classifiers.
^{[7]} - In view of this, stochastic gradient descent offers a lighter-weight solution.
^{[8]} - This generalized stochastic algorithm is also called mini-batch stochastic gradient descent and we simply refer to them as stochastic gradient descent (as generalized).
^{[8]} - There are other practical reasons that may make stochastic gradient descent more appealing than gradient descent.
^{[8]} - Besides, stochastic gradient descent can be considered as offering a regularization effect especially when the mini-batch size is small due to the randomness and noise in the mini-batch sampling.
^{[8]} - This is in fact an instance of a more general technique called stochastic gradient descent (SGD).
^{[9]} - This chapter provides background material, explains why SGD is a good learning algorithm when the training set is large, and provides useful recommendations.
^{[9]} - Stochastic gradient descent is an optimization algorithm which improves the efficiency of the gradient descent algorithm.
^{[10]} - Similar to batch gradient descent, stochastic gradient descent performs a series of steps to minimize a cost function.
^{[10]} - After randomization of the data set, stochastic gradient descent performs gradient descent based on one example, and start to change the cost function.
^{[10]} - However in stochastic gradient descent, as one example is processed per iteration, thus there is no guarantee that the cost function reduces with every step.
^{[10]} - This is in fact an instance of a more general technique called stochastic gradient descent.
^{[11]} - This can perform significantly better than true stochastic gradient descent because the code can make use of vectorization libraries rather than computing each step separately.
^{[12]} - Asynchronous Stochastic Gradient Descent (ASGD) is widely adopted to fulfill this task for its efficiency, which is, however, known to suffer from the problem of delayed gradients.
^{[13]} - We propose a novel technology to compensate this delay, so as to make the optimization behavior of ASGD closer to that of sequential SGD.
^{[13]} - The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency.
^{[14]} - Second, for high-dimensional linear regression, using a variant of the SGD algorithm, we construct a debiased estimator of each regression coefficient that is asymptotically normal.
^{[14]} - This paper is a step towards developing a geometric understanding of a popular algorithm for training deep neural networks named stochastic gradient descent (SGD).
^{[15]} - We built upon a recent result which observed that the noise in SGD while training typical networks is highly non-isotropic.
^{[15]} - Stochastic gradient descent is a method to find the optimal parameter configuration for a machine learning algorithm.
^{[16]} - Stochastic gradient descent attempts to find the global minimum by adjusting the configuration of the network after each training point.
^{[16]} - On the other hand, stochastic gradient descent can adjust the network parameters in such a way as to move the model out of a local minimum and toward a global minimum.
^{[16]} - However, SGD’s gradient descent is biased towards the random selection of a data instance.
^{[17]} - Moreover, GSGD has also been incorporated and tested with other popular variations of SGD, such as Adam, Adagrad and Momentum.
^{[17]} - The guided search with GSGD achieves better convergence and classification accuracy in a limited time budget than its original counterpart of canonical and other variation of SGD.
^{[17]} - The locking mechanism in this case is the aggregation after each pass through the data and makes mini-batch SGD synchronous in nature.
^{[18]} - A distributed adaptation of mini-batch SGD, where each node in a system computes on a single mini-batch, is also a synchronous approach.
^{[18]} - Parallel SGD, introduced by Zinkevich et al.
^{[18]} - In practice, Parallel SGD is a Data Parallel method and is implemented as such.
^{[18]} - This process is called Stochastic Gradient Descent (SGD) (or also sometimes on-line gradient descent).
^{[19]} - Stochastic gradient descent (SGD) takes this idea to the extreme--it uses only a single example (a batch size of 1) per iteration.
^{[20]} - Given enough iterations, SGD works but is very noisy.
^{[20]} - Stochastic gradient descent often does not need more than 1-to-10 passes through the training dataset to converge on good or good enough coefficients.
^{[21]} - The updates for each training dataset instance can result in a noisy plot of cost over time when using stochastic gradient descent.
^{[21]} - SGD does away with this redundancy by performing one update at a time.
^{[22]} - While batch gradient descent converges to the minimum of the basin the parameters are placed in, SGD's fluctuation, on the one hand, enables it to jump to new and potentially better local minima.
^{[22]} - On the other hand, this ultimately complicates convergence to the exact minimum, as SGD will keep overshooting.
^{[22]} - Mini-batch gradient descent is typically the algorithm of choice when training a neural network and the term SGD usually is employed also when mini-batches are used.
^{[22]} - Before explaining Stochastic Gradient Descent (SGD), let’s first describe what Gradient Descent is.
^{[23]} - Hence, in Stochastic Gradient Descent, a few samples are selected randomly instead of the whole data set for each iteration.
^{[23]} - This problem is solved by Stochastic Gradient Descent.
^{[23]} - In SGD, it uses only a single sample, i.e., a batch size of one, to perform each iteration.
^{[23]} - Stochastic gradient descent comes to our rescue !!
^{[24]} - Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable).
^{[25]} - To economize on the computational cost at every iteration, stochastic gradient descent samples a subset of summand functions at every step.
^{[25]} - This can perform significantly better than "true" stochastic gradient descent described, because the code can make use of vectorization libraries rather than computing each step separately.
^{[25]} - The convergence of stochastic gradient descent has been analyzed using the theories of convex minimization and of stochastic approximation.
^{[25]} - What’s the difference between gradient descent and stochastic gradient descent?
^{[26]} - Before understanding the difference between gradient descent and stochastic gradient descent?
^{[26]} - SGD has been successfully applied to large-scale and sparse machine learning problems often encountered in text classification and natural language processing.
^{[27]} - Strictly speaking, SGD is merely an optimization technique and does not correspond to a specific family of machine learning models.
^{[27]} - The class SGDClassifier implements a plain stochastic gradient descent learning routine which supports different loss functions and penalties for classification.
^{[27]} - SGD fits a linear model to the training data.
^{[27]}

### 소스

- ↑
^{1.0}^{1.1}^{1.2}Stochastic Gradient Descent — Orange Visual Programming 3 documentation - ↑
^{2.0}^{2.1}^{2.2}^{2.3}Unsupervised Feature Learning and Deep Learning Tutorial - ↑
^{3.0}^{3.1}^{3.2}^{3.3}Stochastic Gradient descent - ↑ What is the difference between Gradient Descent and Stochastic Gradient Descent?
- ↑
^{5.0}^{5.1}^{5.2}Directional Analysis of Stochastic Gradient Descent via von... - ↑
^{6.0}^{6.1}^{6.2}11.4. Stochastic Gradient Descent — Dive into Deep Learning 0.15.1 documentation - ↑
^{7.0}^{7.1}^{7.2}^{7.3}Stochastic Gradient Descent (SGD) with Python - ↑
^{8.0}^{8.1}^{8.2}^{8.3}Gradient descent and stochastic gradient descent from scratch — The Straight Dope 0.1 documentation - ↑
^{9.0}^{9.1}Stochastic Gradient Descent Tricks - ↑
^{10.0}^{10.1}^{10.2}^{10.3}Stochastic gradient descent - ↑ Stochastic Gradient Descent Tricks
- ↑ scikit-learn: Batch gradient descent versus stochastic gradient descent
- ↑
^{13.0}^{13.1}Asynchronous Stochastic Gradient Descent with Delay Compensation - ↑
^{14.0}^{14.1}Chen , Lee , Tong , Zhang : Statistical inference for model parameters in stochastic gradient descent - ↑
^{15.0}^{15.1}A Geometric Interpretation of Stochastic Gradient Descent Using Diffusion Metrics - ↑
^{16.0}^{16.1}^{16.2}Stochastic Gradient Descent - ↑
^{17.0}^{17.1}^{17.2}Guided Stochastic Gradient Descent Algorithm for inconsistent datasets - ↑
^{18.0}^{18.1}^{18.2}^{18.3}A parallel and distributed stochastic gradient descent implementation using commodity clusters - ↑ CS231n Convolutional Neural Networks for Visual Recognition
- ↑
^{20.0}^{20.1}Reducing Loss: Stochastic Gradient Descent - ↑
^{21.0}^{21.1}Gradient Descent For Machine Learning - ↑
^{22.0}^{22.1}^{22.2}^{22.3}An overview of gradient descent optimization algorithms - ↑
^{23.0}^{23.1}^{23.2}^{23.3}Stochastic Gradient Descent (SGD) - GeeksforGeeks - ↑ Stochastic Gradient Descent — Clearly Explained !!
- ↑
^{25.0}^{25.1}^{25.2}^{25.3}Stochastic gradient descent - ↑
^{26.0}^{26.1}What’s the difference between gradient descent and stochastic gradient descent? - ↑
^{27.0}^{27.1}^{27.2}^{27.3}1.5. Stochastic Gradient Descent — scikit-learn 0.23.2 documentation

## 메타데이터

### 위키데이터

- ID : Q7617819