Time series analysis to predict future points on Stan

Overview

Before, I made the simple local level model to time series data. At that article, I just showed the sampled points traced the data. This time, I also do sampling to predict the following points of the data.



Roughly, on the image above, the blue points are data you already have and the red points are the predict target. The purpose of this article is to make model by blue points, data and predict red points, the values of future.

Local level model to time series data on Stan

Overview

On the articles below, I tried local level modeling to time series data on Edward and am still struggling.

Time series analysis on TensorFlow and Edward: local level model

Deep learning and Machine learning methods blog

Time series analysis on TensorFlow and Edward: local level model:P.S. 1

On the article below, I tried to analyze time series data with local level model. On Stan, I could do it before without problem. But on Edward and TensorFlow, I have been struggling. Deep learning and Machine learning methods blog From the situation above, although it doesn't work well yet, I got some progress.

On this article, I’ll express by Stan what I wanted on Edward. In a nutshell, I’ll write local level model to time series data on Stan.

Time series analysis on TensorFlow and Edward: local level model:P.S. 1

Overview

On the article below, I tried to analyze time series data with local level model. On Stan, I could do it before without problem. But on Edward and TensorFlow, I have been struggling.

Time series analysis on TensorFlow and Edward: local level model

Deep learning and Machine learning methods blog

From the situation above, although it doesn’t work well yet, I got some progress.

Time series analysis on TensorFlow and Edward: local level model

Overview

To review the time series analysis from the basic points, I tried to do state space modeling with TensorFlow and Edward. And I’m at a loss.
The main purposes are these two.

• review the time series analysis from the basic points
• try to check how to do that on Edward and TensorFlow

Classification by deep neural network using tf.estimator of TensorFlow

Overview

On the article below, I checked how to write deep neural network by tf.estimator. But it was regression case.

tf.estimator of TensorFlow lets us concisely write deep neural network

On this article, I'll re-write the simple deep neural network model to iris data by tf.estimator. From official page, TensorFlow's high-level machine learning API (tf.estimator) makes it easy to configure, train, and evaluate a variety of machine learning models. By comparing with the original code, I'll check how much it becomes concise and how to use tf.estimator.

Here, just in case, I’ll check the classification case. This is totally same as the official page’s tutorial and actually, the difference between regression and classification about the aspect of code is quite few. But classification and regression are one of the most basic tasks on machine learning and data science. So I’ll do it by myself.

tf.estimator of TensorFlow lets us concisely write deep neural network

Overview

On this article, I’ll re-write the simple deep neural network model to iris data by tf.estimator. From official page,

TensorFlow’s high-level machine learning API (tf.estimator) makes it easy to configure, train, and evaluate a variety of machine learning models.

By comparing with the original code, I’ll check how much it becomes concise and how to use tf.estimator.

Simple example of how to use TensorBoard

Overview

On this article, through the simple regression, I’ll show how to observe the parameter’s behavior on TensorBoard.

TensorBoard is cool visualizing tool and by using it, our debug to model can be easier.

How to use TensorBoard through arithmetic calculation on TensorFlow

Overview

Through basic arithmetic operations, let’s check how those are expressed on TensorBoard.

It has two main points.
One, check the main calculation function on TensorFlow.
Two, check how it is expressed on TensorBoard.

TensorFlow deals with Tensor, leading us to use TensorFlow’s methods for mathematical operations. Simply, here, I’ll use some of them. And, TensorBoard is the tool to check the graph and other information graphically. As a simple check, I’ll show how those operations are expressed visually on that.

Edward modeling to artificial data with random effects

Overview

By Edward, I’ll try to make the model with random effect.
There are some ways to fulfill that. On this article, I’ll follow the style that the Edward tutorial takes.

• Edward Tutorial

Fashion-MNIST exploring using Keras and Edward

Overview

On the article, Fashion-MNIST exploring, I concisely explored Fashion-MNIST dataset.

We can get access to the dataset from Keras and on this article, I’ll try simple classification by Edward.

Simple Baysian Neural Network with Edward

Overview

Edward can enable us to convert TensorFlow code to Baysian one. I’m not used to Edward. So for the training, I’m tackling with converting some TensorFlow code to Edward one. On this article, I tried to convert simple neural network model to Baysian neural network one.

The purpose of this article is to convert the TensorFlow code I posted before to Baysian one by Edward.

Baysian neural network model

By Edward, we can relatively easily convert the model using TensorFlow to probabilistic one.
The regression model for iris data is from the article below.

Simple regression model by TensorFlow

Neural network is composed of input, hidden and output layers. And the number of hidden layers is optional. So the simplest network architecture has just one hidden layer. On this article, I'll make the simplest neural network for regression by TensorFlow.

In a nutshell, the model is to predict one target value from three features. About the details, please check the article.

Simple regression by Edward: variational inference

Overview

Edward is one of the PPL(probabilistic programming language). This enables us to use variational inference, Gibbs sampling and Monte Carlo method relatively easily. But it doesn’t look so easy. So step by step, I’ll try this.

On this article, simple regression, tried on the article Simple Bayesian modeling by Stan, can be the nice example. So I did same things by Edward, using variational inference.

How to complement missing values in data on Python

As data pre-processing, we frequently need to deal with missing values. There are some ways to deal with those and one of them is to complement those by representative values.

On Python, by scikit-learn, we can do it.
I'll use air quality data to try it.

To prepare the data, on R console, execute the following code on your working directory.

write.csv(airquality, "airquality.csv", row.names=FALSE)

TensorFlow Machine Learning Cookbook:book memo

Recently, TensorFlow Machine Learning Cookbook has been published in Japan and I took one.

Image generator of Keras: to make neural network with little data

Keras has image generator which works well when we don’t have enough amount of data. I’ll try this by simple example.

Overview

To make nice neural network model about images, we need much amount of data. In many cases, the shortage of data can be one of the big obstacles for goodness.
Keras has image generator and it can solves the problem.

InceptionV3 Fine-tuning model: the architecture and how to make

Overview

InceptionV3 is one of the models to classify images. We can easily use it from TensorFlow or Keras.
On this article, I’ll check the architecture of it and try to make fine-tuning model.

There are some image classification models we can use for fine-tuning.
Those model’s weights are already trained and by small steps, you can make models for your own data.

About the fine-tuning itself, please check the followings.

• How to make Fine tuning model by Keras
• VGG19 Fine-tuning model

Or TensorFlow and Keras have nice documents of fine-tuning.

From TensorFlow

• How to Retrain Inception’s Final Layer for New Categories

From Keras

• Applications

How to interpret the summary of linear regression with log-transformed variable

How should we interpret the coefficients of linear regression when we use log-transformation?

On the area of econometrics and data science, we sometimes use log-transformed weights for linear regression. Usually, one of the advantages of linear regression is that we can easily interpret the outcome. But by log-transformation, how should we interpret the outcome?

Overview

In many cases, we adopt linear regression to analyze data. That lets us understand how influential each feature is.

So when we use it, to make the way of interpretation easy, we want as simple features as possible. If you transform the features, you need to adjust your interpretation to that.

I got started with JupyterLab

I just got started with JupyterLab.

From the official page, JupyterLab is

An extensible environment for interactive and reproducible computing, based on the Jupyter Notebook and Architecture.

As you know, Jupyter is very useful tool. To use it efficiently directly improves your efficiency of work. JupyterLab showed the possibility at least to me.

Hierarchical Bayesian model's parameter Interpretation on Stan

Usually, Hierarchical Bayesian model has many parameters. So apparently, the interception to the sampled point’s statistical information looks complex.

On the article below, I made a Hierarchical Bayesian model to the artificial data. Here, by using almost same but simpler data, I’ll make a model and try to interpret.

Hierarchical Bayesian model by Stan: Struggling

I'll try to make Hierarchical Bayesian model to the artificial data by Stan. Hierarchical Bayesian model lets us write the model with a high degree of freedom.

Hierarchical Bayesian model by Stan: Struggling

I’ll try to make Hierarchical Bayesian model to the artificial data by Stan. Hierarchical Bayesian model lets us write the model with a high degree of freedom.

From Wikipedia,

Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method.[1] The sub-models combine to form the hierarchical model, and the Bayes’ theorem is used to integrate them with the observed data, and account for all the uncertainty that is present. The result of this integration is the posterior distribution, also known as the updated probability estimate, as additional evidence on the prior distribution is acquired.

Bayesian modeling to data with heteroscedasticity by Stan

Before, I wrote about the data with heteroscedasticity.

What is heteroscedasticity and How to check it on R

Linear regression with OLS is simple and strong method to analyze data. By the coefficients, we can know the influence each variables have. Although it looks easy to use linear regression with OLS because of the simple system from the viewpoint of necessary code and mathematics, it has some important conditions which should be kept to get proper coefficients and characteristics.

How to deal with heteroscedasticity

On the article below, I wrote about heteroscedasticity. Linear regression with OLS is simple and strong method to analyze data. By the coefficients, we can know the influence each variables have. Although it looks easy to use linear regression with OLS because of the simple system from the viewpoint of necessary code and mathematics, it has some important conditions which should be kept to get proper coefficients and characteristics.

This time, I’ll make the model again but with Python and Stan.

Bayesian multiple regression by Stan

Overview

On the article, Simple Bayesian modeling by Stan, I made a simple linear regression by Stan and PyStan. So, as an extension of it, I made multiple regression model on the same manner to show how to do Bayesian modeling roughly.

Simple Bayesian modeling by Stan

Overview

About Bayesian modeling, we can use some languages and tools. BUGS, PyMC, Stan. On this article, I made simple regression model by using Stan from Python.

Similar image finder by CNN and Distance

Overview

On this article, I’ll show one of the methods to find similar images to some specific target image.

Usually, when we try to make the system to find some similar items, we have some choices and should choose one or some of them in response to the purpose. Here, I’ll adapt distance-based method using supervised learning model’s prediction.

For example, when we try to find the images which are similar to the leftmost image, the other images below are picked up by this.

Perceptron by scikit-learn

Overview

I sometimes use Perceptron, one of the machine learning algorithms, as practice of algorithm writing from scratch.

But in many cases, it is highly recommended to use machine learning library. Although there are not many cases in practice that we use Perceptron, it is not wasted to know how to write Perceptron by the library, concretely scikit-learn.

On this article, I’ll show how to write Perceptron by scikit-learn.

Stats package on Golang

When we deal with data on the meaning of data analysis, data science, and machine learning, Go’s statistics package does a good job.

On the area of data science and machine learning, people usually use Python and R. On the internet, we can see just a few amount of information about data science with Go.

So I’ll leave concise memo about that.
Here I’ll introduce how to use basic statistics package.

How to deal with heteroscedasticity

On the article below, I wrote about heteroscedasticity.

What is heteroscedasticity and How to check it on R

Linear regression with OLS is simple and strong method to analyze data. By the coefficients, we can know the influence each variables have. Although it looks easy to use linear regression with OLS because of the simple system from the viewpoint of necessary code and mathematics, it has some important conditions which should be kept to get proper coefficients and characteristics.

Roughly, with heteroscedasticity, we can’t get OLS’s nice feature, unbiasedness. And plot and some tests such as Breusch-Pagan test reveal the existence of heteroscedasticity.

After knowing the problem, of course we need to know how to solve it.
Here on this article, I’ll write about how to deal with this heteroscedasticity.

I’ll use same data here as the article above.

What is heteroscedasticity and How to check it on R

Linear regression with OLS is simple and strong method to analyze data. By the coefficients, we can know the influence each variables have.

Although it looks easy to use linear regression with OLS because of the simple system from the viewpoint of necessary code and mathematics, it has some important conditions which should be kept to get proper coefficients and characteristics.

On this article, I’ll show the way to check heteroscedasticity.

Simple tutorial to write deep neural network by TensorFlow

Overview

On this article, I’ll show simple deep neural network(DNN) model for regression by TensorFlow.

TensorFlow is open source library from Google. From the official web site,

TensorFlow™ is an open source software library for numerical computation using data flow graphs.

From wikipedia,

TensorFlow is an open-source software library for machine learning across a range of tasks. It is a system for building and training neural networks to detect and decipher patterns and correlations, analogous to (but not the same as) human learning and reasoning.[3] It is used for both research and production at Google,‍[3]:min 0:15/2:17 [4]:p.2 [3]:0:26/2:17 often replacing its closed-source predecessor, DistBelief.

It lets us make neural network relatively easily. But different from keras, this needs proper knowledge of the things you want to make.
This article is almost simple tutorial to make deep neural network model for regression.

You can know the followings on this article.

• What is deep neural network?
• How do we write deep neural network model by TensorFlow

Simple regression model by TensorFlow

Overview

Neural network is composed of input, hidden and output layers. And the number of hidden layers is optional. So the simplest network architecture has just one hidden layer.

On this article, I’ll make the simplest neural network for regression by TensorFlow.

From the official web site,

TensorFlow™ is an open source software library for numerical computation using data flow graphs.

This makes it easier to make shallow and deep neural network and other machine leaning algorithms. Through the simple trial, we can learn about TensorFlow and the system of neural network.

About the Tensorflow itself, please check the article below.

• Simple guide for Tensorflow

VGG16 Fine-tuning model

Overview

On the article, VGG19 Fine-tuning model, I checked VGG19’s architecture and made fine-tuning model. On the same way, I’ll show the architecture VGG16 and make model here.

There are some image classification models we can use for fine-tuning.
Those model's weights are already trained and by small steps, you can make models for your own data.

About the fine-tuning itself, please check the followings.

• How to make Fine tuning model by Keras
• VGG19 Fine-tuning model

Making linear regression model by R

Overview

When we make model by data science, machine learning method, it’s not simple process such as “just throw data into SVM”. Getting, checking, processing, modeling, evaluation. There are many steps you need to care about.

On this article, by making regression model on R, I’ll show the example of part of the process.

Simple guide to kNN

Personally, I like kNN algorithm much. Because kNN, k nearest neighbors, uses simple distance method to classify data, you can use that in the combination with other algorithms. It can also be one of the first step to study machine learning algorithms because of the simplicity.

On the following articles, I wrote about kNN. But although I myself don’t know the reason, I’ve never touched the simplest usage of kNN, meaning how to use kNN of sklearn’s library.

• kNN by Golang from scratch
• How to write kNN by TensorFlow
• Speed up naive kNN by the concept of kmeans
• CNN + KNN model accuracy

How to write kNN by TensorFlow

Overview

How do we write machine learning algorithms with TensorFlow?
I usually use TensorFlow only when I write neural networks. But actually TensorFlow is not only for that. It also can be used to write other machine leaning algorithms.
On this article, I tried to roughly write kNN algorithm by TensorFlow.

The reason to try kaggle and how you do

Overview

I sometimes hear as the answer to the question, “What should I do as study of data science?”, the importance of kaggle.

Personally, I agree with the idea that he/she tries kaggle as early as possible.
Why is kaggle awesome to improve the knowledge of data science/mach learning? I summarize the points of kaggle’s advantages from the viewpoint of studying.

Observation of Beta distribution

Overview

PRML(Pattern Recognition and Machine leaning) is one of the best text books about machine learning. I review it from time to time.
As one of the reviews, I write down some notes of part of it.
This article is about Beta distribution, which is shown on chapter 2 on PRML.

Fashion-MNIST exploring

Overview

Fashion-MNIST is mnist-like image data set. Each data is 28x28 grayscale image associated with fashion. Literally, this is fashion version of mnist.

I'm thinking to use this data set on small experiment from now on. So, for the future, I checked what kind of data fashion-MNIST is.

On the article below, I explored from the viewpoint of Bayes.

Fashion-MNIST exploring using Keras and Edward

On the article, Fashion-MNIST exploring, I concisely explored Fashion-MNIST dataset. We can get access to the dataset from Keras and on this article, I'll try simple classification by Edward. I'll use Fashion-MNIST dataset. Fasion-MNIST is mnist like data set. You can think this as the fashion version of mnist.

VGG19 Fine-tuning model

Overview

On the article, How to make Fine tuning model, I made fine-tuning models by some pre-trained models. At that time, I didn't write about the pre-trained model's architecture and the train target area based on it.

This time, I foucused on the VGG19 as pre-trained model. And in a nutshell, I tried to make fine-tuning model in better manner, checking some important points.

How to make Fine tuning model by Keras

Overview

Fine-tuning is one of the important methods to make big-scale model with a small amount of data.

Usually, deep learning model needs a massive amount of data for training. But it is not always easy to get enough amount of data for that. To be added, in many cases, it takes much time to make model from the viewpoint of training. I know you don’t like to see one epoch of training using the time from sunrise to sunset. In some areas like image classification, you can use fine-tune method to solve this situation.

For example, when you try to make image classification model, very deep CNN model works well(sometimes and other time not). To make that kind of model, it is necessary to prepare a huge amount of data. However, by using the model trained by other data, it is enough to add one or some layers to that model and train those. It saves much time and data.

Here, I show this type of method, fine-tuning, by Keras.

Data visualization by Golang

Overview

Usually when I plot data’s behavior to check it and to decide the approach, I use Python, matplotlib. Actually these days this is one of the best answer from the viewpoint of data science. But for these 3 or 4 weeks, I have been using Go and as a data scientist, I feel obligation to know how to plot data even at a basic level.
This is basic plot note about Golang.

Speed up naive kNN by the concept of kmeans

Overview

About prediction, kNN(k nearest neighbors) is very slow algorithm, because it calculates all the distances between predict target and training data point on the predict phase.
By adding some process, I tried to make the naive kNN speed up and checked how much the time and accuracy changes.

kNN by Golang from scratch

Overview

I wrote kNN(k nearest neighbors), one of the machine learning algorithms, by Go.
Go has some machine learning packages but it is hard to find the information of how to write machine learning algorithms by Go. So I stepwise introduce how to. This time kNN.
This article is to understand how the algorithm. So I don’t use some elements to improve the accuracy if it disturbs the understanding essential points.

kmeans by Golang from scratch

Overview

Here, I introduced how to write kmeans, one of the machine learning algorithms, on Go. I’m almost new to Go and this is coding exercise for me through machine learning algorithms.
Go has some machine learning packages. But I couldn’t find the information about how to write machine learning algorithms from scratch. So, I stepwise introduce those.
Those I write here is not for practical use but for understanding algorithms by reading and writing, leading me to set priority on making the code simpler by sacrificing accuracy-improving elements if those are not very easy.

Perceptron by Golang from scratch

Overview

I tried perceptron, almost “Hello world” in machine learning, by Golang.
Go has matrix calculation library like numpy on Python. But this time I just used default types.

Usually on machine leaning, R and Python are frequently used and almost all from-scratch code of machine learning is shown by those or by C++. So I just tried this “Hello world”.

How to use gonum/matrix (Golang package)

When I started to learn about Golang, the first obstacle to use that for machine learning was matrix data manipulation. On Python, you can use numpy, pandas. On Go, on some machine learning package uses gonum/matrix. So I just checked how to use.

Overview

I make a summary about gonum/matrix’s basic usage.

Understand how to use keras's functional API

Overview

keras is awesome tool to make neural network. Being compared with Tensorflow, the code can be shorter and more concise. If you want to enter the gate to neural network, deep learning but feel scary about that, I strongly recommend you use keras.

keras has two types of writing ways. Here I introduce one of them, functional API.

How Dropout works on Neural Network

Overview

Dropout is one of the good techniques to make good neural network model. The system of it is very simple.

Perceptron from scratch

Overview

There are good libraries to make machine learning model and usually, it’s enough to use those to attain the goal you set on the model.

It’s not necessary to write algorithm by yourself. To say precisely, to write and use your full-scratch written model makes more bugs than prevalent library’s one. So you should use prevalent libraries except for the time that those don’t fulfill what you want to get.

But to deepen your understandings and knowledge to machine leaning, writing existing algorithm by yourself is very good trial.
Here, I show how to write perceptron algorithm.

Practical hack to make deep learning model

Overview

Neural network has a lot of flexibility in its design. You can choose and set many components and options. Because of that, to make more optimized network, you need to know and care about the procedures to adjust those to update your network efficiently.
Here, I arranged neural network’s components and in which procedure those should be adjusted.

Re-try CNN + KNN model

Overview

When I tried CNN + KNN model before, the training epoch was not enough(50) to check the characteristics. This time I trained 200 epoch on the CNN phase.

Simple guide to Neural Network

What is Neural network?

Neural network is an algorithm which make input go through at least one hidden and output layers to output.
Graphically it is like below.

CNN + KNN model accuracy

Overview

On the contest site like Kaggle, we can see many trials and good scores by the combination of some methods.
For example, you can get scores by logistic regression and lasso regression. You can make xgboost model by using those scores.
This time, about cifar-10, I make CNN model. And by using the score, I check KNN scores.

The pragmatic procedure of making CNN model

Overview

On the image classification modeling, you need to understand how good your model is, meaning not absolute accuracy itself but relative meaning of the accuracy.

This is the example. Your first trial model's validation accuracy is 0.6. How do you think about it?
Without knowing the unique label number, ratio, and the data's difficulty, only answer you can return is "I don't know".
To evaluate the model, not only the absolute accuracy but also the base score to compare with are necessary.

If the modeling trial and error don't take much time, you can feel the scale of goodness and accuracy by many trial samples. But usually image classification model takes much time to make themselves.
How do we do the shortcut?

How to write diverged type neural network by keras

How to write Diverged neural network

Overview

Simple style neural network as below is easy to write by deep learning frame work. 

This time, I make diverged neural network whose route to output is diverged and merged. The image of this is like below.

The purpose of this article is following two points.

• see how to write diverged type neural network
• see how accurate and good this type of model is

I used keras to write. Although it is bit annoying to write this kind of neural network compared with simple type, keras makes diverged type of model in relatively easy manner.
About the model's characteristics and accuracy, it’s difficult to judge, because there is no simple model which is relevant to the diverged model. So, we can just check roughly.

sigmoid function

Sigmoid function is frequently used in machine learning, because it can approximates discontinuous function like step function.
This function is very simple as you can see.

In the code, you can write like this.

import numpy as np

def sig(x):
    return 1 / (1 + np.exp(-x))

And by plotting.

import matplotlib.pyplot as plt

x = list(range(-100, 100))
y = [sig(i) for i in x]
plt.plot(x, y)
plt.show()

On this plot, the inclination looks too strong.
By focusing on small range, we check this.

x = list(range(-10, 10))
y = [sig(i) for i in x]
plt.plot(x, y)
plt.show()

By this, we can see how it changes.
Sigmoid function has following characteristics.

• When the input is equal to 0, the output is 1/2.
• This function is monotonically increasing.
• This function is point symmetry at (0, 1/2)

Googles's Tensorflow Object Detection API trial

Try Google’s TensorFlow Object Detection API

Overview

Google sent to the world awesome object detector.
When I tried object detection before by myself, I strongly felt it was hard job and even small trial took much time.
Not to be late to the growing technology about image detection, I tried object detection tutorial today.

Method for efficient neural network

Overview

Usually, neural network’s training takes much time and doesn’t go well. There are some ways to make that efficiently go.
Here, I list up those and summarize.
By using those method, the training go well and good model can be made.

Plot some graph at once by matplotlib

How to do subplot

Overview

When we make machine learning model and check how accurate the predictions are, we frequently plot those.
Plotting some graphs at the same time is very useful to compare outcomes. By matplotlib, those can be done.

How to use Inception v3

Low cost image classification by CNN, convolutional neural network

Overview

These days, CNN(convolutional neural network) is almost regarded as the best answer to classify images.
But it has many rules.

• it needs huge amount of images
• it takes much time to train
• it needs slow and gradual steps to find good network model to attein the goal
• it needs high spec environment to do try-and-error

Of course, there are free data sets and kinda sample network which works easily in short time. But at the case you practically make model to solve some practical problem personaly or oficilally, those restrictions can face with you.
The combination of Inception v3 model and fine tune can solve the point.

Basic classification example by logistic regression

Basic classification example

Overview

I make classification model of free wine data, following how to deal with it step by step.

Convolutional neural network scale experiment by keras

Overview

It is not easy to understand about convolutional neural network how the goodness changes when the nodes each layer has, layer’s number and other factors change.

For practical use of convolutional neural network, I experimented some types of convolutional neural network.

Breakout by tensorflow model

Overview

I made a Tensorflow model of breakout by the data which is from my playing.
The purpose of this is to visually observe how outcome of the prediction works. So this time ‘theoretical accuracy’ should be left behind.
I just made simple and easy model without thinking about details and tried to make the model play breakout like the following image.

The one I used as breakout is from address.
breakout

Simple guide for Tensorflow

Overview

This article is to roughly understand Tensorflow and make easy model.
These days if you are machine-oriented person, you can't pass even a day without hearing the name of Tensorflow. This is very useful tool but not so easily approachable.
Let't check what Tensorflow is and how you can use it.

Convolutional neural network by keras

Make convolutional neural network model for mnist in keras

Overview

Convolutional neural network is one of the best solutions about image classification. In keras, it is relatively easy to make model.

Simple keras trial

Simple keras trial

Overview

By making simple newral network, I try to use keras.