An RFC (request for comments) for Vue.js was published that explains the
plan for a new Function API. Following that, a plugin was created that allows the proposed Function API to be used in current Vue applications: vue-function-api.
I thought I would experiment with the Function API by building a mini app.
Function API Installation
The base app was created using vue cli, and the vue-function-api plugin installed using yarn:
$ vue create janken
$ yarn add vue-function-api
Then the plugin installed explicitly:
import Vue from 'vue'
import { plugin } from 'vue-function-api'
Vue.use(plugin)
The current API (Standard API) still works as usual, and it is even possible to use a hybrid approach (Function API + Standard API).
The app I decided to build was Janken, or in English: Rock, Scissors, Paper.
In this app there are 4 features:
The player can choose their hand
The computer chooses their hand and a winner is calculated
The total amount of points (wins) for each player are shown
The first change from the Standard API is that a setup option is used to set up
the component logic. If you need to use props they are passed to setup as an argument (more
info).
The score data would have previously be stored in the data option, which is not used in the Function API.
Instead the data is stored by using the value API. Data and functions
that are used in the template are returned from the setup option.
The next task was to enable the player to choose their hand. Using the Standard API this can be done using the
methods option. In the Function API the same can be done using a function.
To set (and also get) the value of playerHand within setupplayerHand.value
must be used.
Computed
The hands are displayed in the UI using emoji. The hand data stored as a string ('rock') is converted
to an emoji ('✊') with the computed API (similar to the Standard API's computed
option). Again this is stored to a variable and returned from setup to be used in the template.
If there are many methods or computed values in the returned object, these can be grouped into a single object and
destructured in the object returned from setup.
After adding the logic for the game and editing the player name I tried refactoring using a technique made possible in the Function API. Using a composition
function the logic (variables and methods) could be extracted to a separate function, and then included in the
object returned from the main setup option.
By doing this the code can be organised more clearly, collecting related code together rather than it being separated
between different options(data, computed, methods, etc) which can happen in the
Standard API. It is also possible to reuse the logic in other components.
Although not used in this app lifecycle
hooks and watchers are
used in a similar way to value and computed and can also be extracted.
The Janken app and code can be seen and used below. It only took a few steps to get started with the Function API, and there are various features I did not use that I'm looking forward to trying. For more information check out the RFC and try it yourself!
This blog will show a new experimental method for data augmentation geared towards bio-science for deep learning. This is important for several reasons. 1: Collecting data is time-consuming especially in collecting large enough observations for training deep learning models. 2: It can be difficult to collect or sample enough observations due to the lack of access or chances to make collections. 3: Collecting observations can only be done at certain times or during certain periods, or the period of time for sampling has passed so the collection of further/more observations are impossible. 4: There are few species available to collect samples from. These are just 4 simple reasons why data augmentation is needed for biological studies.
Methods for Data Augmentation
The simplest method for data augmentation is to match the generated data both statistically and logically to the observed data. This means that the data that is generated should have a similar look and feel of the real-world data. The two data sets should have similar distributions, mean, modes, etc. to ensure that the data truly simulates the observed sequences. The simulated data should also be logically like the data that is observed. This means that the simulated data should not have outliers model into it as this will confuse any model. The augmented data should flow alongside the observations and almost mirror each observation. But, just copying the real observations is not an appropriate method for data augmentation. The observations should change slightly. For example, common methods for data augmentations in CNN are image rotation, flipping, cropping, changing color, etc. to create “new” unseen images for a CNN to be trained on. This is also true for numerical data, but not as easy as just flipping the numbers from 10 to 01 as they are not the same.
There are very few methods that exist for data augmentation for numerical data. There are even fewer geared specifically towards biodata or biostudies. This blog will show a new method for generating near-infinite observations based simply on the minimum and maximum observations in a data set.
The data set that I am using is a publicly available data set of Body Measurements (BDIMS)(Heinz, Peterson, Johnson, & Kerk, 2003). This data set is the girth and skeletal measurement of 247 men and 260 women.
Now let's get into the coding aspect of it:
CODE
First, let's get all the import statements out of the way.
import numpy as np
import pandas as pd
%matplotlib inline
import matplotlib.pyplot as plt
import pymc3 as pm
import theano
from statsmodels.formula.api import glm as glm_sm
import statsmodels.api as sm
from pandas.plotting import scatter_matrix
from random import randint
Next, we need to do some quick examination of the data we downloaded.
# Read the data in from the csv file
data = pd.read_csv("bdims.csv")
print(data.columns)
Much nicer. Now we only want to look at one subject as this is biological data. So we will filter out females from males and just look at males. This process will work on both sexes as the steps will be the same, but doing both at the same time will yield poor results as there are biological differences between males and females in general.
# Split between male and female
male_mask = filter_data['sex'] > 0
male = filter_data[male_mask]
female = filter_data[~male_mask]
# After sperating the two exes lets drop the sex collumn as we dont need it
male = male.drop(['sex'], axis=1)
male.describe()
hgt wgt che.gi hip.gi kne.gi thi.gi ank.gi wri.gi wai.gi
count 247.000000247.000000247.000000247.000000247.000000247.000000247.000000247.000000247.000000
mean 177.74534478.144534100.98987997.76315837.19554756.49797623.15910917.19028384.533198
std 7.18362910.5128907.2090186.2280432.2729994.2466671.7290880.9079978.782241min157.20000053.90000079.30000081.50000031.10000046.80000016.40000014.60000067.10000025% 172.90000070.95000095.95000093.25000035.75000053.70000022.00000016.50000077.90000050% 177.80000077.300000101.00000097.40000037.00000056.00000023.00000017.10000083.40000075% 182.65000085.500000106.050000101.55000038.45000059.15000024.30000017.85000090.000000max198.100000116.400000118.700000118.70000045.70000070.00000029.30000019.600000113.200000
Now with the first step of preprocessing, we can get into the process of creating the dataset from only two points! These two points will be the minimum and maximum based on height. Height is chosen because this variable is the dominating variable in biology and bio-mass. Weight is normally heavily dependant on height (pun intended). The dependent variable will be weight. (X = height Y = weight).
So let's find the smallest and largest person in the dataset.
# Find the smallest item based on height # Create a new dataframe of the smallest and larget
min_max_male = pd.DataFrame(male[male.hgt == male.hgt.max()])
min_max_male = min_max_male.append(male[male.hgt == male.hgt.min()])
# Sort by height
sort_min_mix_male = min_max_male.sort_values('hgt')
print(sort_min_mix_male)
hgt wgt che.gi hip.gi kne.gi thi.gi ank.gi wri.gi wai.gi
105157.258.491.691.335.555.020.816.480.6126198.185.596.994.939.254.427.517.982.5
ax1 = min_max_male.plot.scatter(x='hgt',y='wgt',c='DarkBlue')
Max Min PlotSo the first and simplest method to interpolation is linear regersion. This will give us a few extra points of missing data.
# Now use linear regression to fill in some of the missing pointsimport numpy as np
from sklearn.linear_model import LinearRegression
x = np.array([min_max_male.hgt.min(),min_max_male.hgt.max()]).reshape((-1, 1))
y = np.array([min_max_male.wgt.min(), min_max_male.wgt.max()])
# Define a linear regerssion model
model = LinearRegression()
model.fit(x, y)
r_sq = model.score(x, y)
print('coefficient of determination:', r_sq)
print('intercept:', model.intercept_)
print('slope:', model.coef_)
coefficient of determination: 1.0
intercept: -45.75941320293397
slope: [0.66259169]
Linear RegressionOk looks fine so far. The blue dots are the original data (min and max) and the red dots are the newly generated data. This makes sense as weight should increase as height increases. But, not really. There are variations in weight because of other factors. Also, 41 new points don't make a deep learning set.
Lets create a few more points:
# Now lets fine tune the hieght veriable by a float instead of a int# We can resue the linerar regression model to generate more data# Go from 41 observations to 409000 observatsions # All equally possible to occure in the real world
current_hgt = min_max_male.hgt.min()
count = 0
large_hgt = []
while current_hgt <= min_max_male.hgt.max():
# increase the height by 0.1 cm
current_hgt +=0.0001
large_hgt.append(current_hgt)
count +=1print(len(large_hgt))
409000# Now using the newlly generated fine scale height lets get the weight
large_pred = []
for h in large_hgt:
new_x = np.array(h).reshape((-1, 1))
pred = model.predict(new_x)
large_pred.append(pred[0])
print(len(large_pred))
409000# Now lest plot everything again
plt.plot(large_hgt, large_pred, 'go')
plt.plot(gen_height, prediction, 'ro')
plt.plot(old_min_hgt, old_min_wgt, 'bo')
plt.plot(old_max_hgt, old_max_wgt, 'bo')
plt.show()
Larger Dataset
As you can see perfectly overlaps and each observation makes sense and is logical.
The blue dots are the original, the red is the first step, and the green is fine-tuned steps.
This jumps from 2 observations (min and max) to 41 observations (fully synthetic) to 409000 observations.
But in the real world, biology does not always follow a linear line
Let's introduce some variability into the data generation!
# Define a new line using all the data from the real data set# Define a linear regerssion model
X = np.array(male.hgt).reshape(-1, 1)
Y = np.array(male.wgt).reshape(-1, 1)
model2 = LinearRegression()
model2.fit(X,Y)
r_sq2 = model2.score(X,Y)
print('coefficient of determination:', r_sq2)
print('intercept:', model2.intercept_)
print('slope:', model2.coef_)
coefficient of determination: 0.28594874074704446
intercept: [-60.95336414]
slope: [[0.78256845]]
# Linear regresion using real data
y_pred = model2.predict(X)
# Now plot all the data
plt.plot(X, y_pred, color='blue', linewidth=3)
plt.plot(male.hgt, male.wgt, 'yo')
plt.plot(large_hgt, large_pred, 'go')
plt.plot(gen_height, prediction, 'ro')
plt.plot(old_min_hgt, old_min_wgt, 'bo')
plt.plot(old_max_hgt, old_max_wgt, 'bo')
plt.show()
Real DataAs you can see the regression line is some what close to the line of data that is generated. It is not perfect and there will be a lot of variability between the two datasets. But seeing that this is only based on two observations, (the min and max) the lines are pretty close. The intercept and slope are close enough to use the ones found from the two points only. So let us continue and make a fully synthetic deep learning dataset from two observations.
# The slope of the line is b, and a is the intercept found from Sklenar linear model# Simple Linear regressoin model Y = a + bX that will be the model for out MCMC
alpha = -45.75941320293397# Intercept
beta = [0.66259169] # Slope
X = np.array(large_hgt)
Y = np.array(large_pred)
print(len(X))
print(len(Y))
409000409000# Weight Histogram
hist = male.hist(column='wgt')
Real Data Histogram
#Normal distribution. mu is the mean, and sigma is the standard deviation.# Seeing that the weight is normally distributed (basically) we can use that knowledge to generate new data via a normally# Distrubuted method#for random.normalvariate(mu, sigma)
std = np.std(X, axis=0)
real_std = np.std(male.wgt, axis=0)
print(std)
print(real_std)
11.80681300528450410.491587167890629
temp_min_max = []
temp_min_max.append(male.wgt.max())
temp_min_max.append(male.wgt.min())
mean = np.mean(temp_min_max)
real_mean = np.mean(male.wgt)
print(mean)
print(real_mean)
85.1578.14453441295547
Looking at the mean and standard deviation they are close enough for this example. Lets make a Million data points for our new dataset! That should be enough for any deep learning dataset.
A Million Data points!Well thats no good. Now to be fair, given a infinate number of samples, it is highly likely that at least for each point there would have been someone that mathces the height and weight on this chart, but that is like using a shotgun to fish. It is not as accurate and not really following the regression line of the real data which means that the dataset is not useful and cannot be used in a deep learning model as it wont learn anything.
So how can we fix this?
Let's perform some rejections by using a concept of banding. So if the observation falls outside the bands it won't get plotted. The bands themselves set up an upper and lower limit so that all predictions will have to fall within these limits. To form these limit expert knowledge of the observed phenomenon is needed especially for only two observations, luckily for us, we have more than two observations so we can define out limits based on the full real dataset.
# Use upper and lower limits to reject samplesdefmake_sample(lower, upper, mean, std):
sample = np.random.normal(mean,std)
if lower < sample < upper:
return sample
else:
make_sample(lower, upper, mean, std)
# Define bands for each interval# The more bands the finer the level of rejection# Each item in the array is defined as# [band lower, band upper, lower limit, upper limit]
band1 = [0, 155, 50, 70]
band2 = [156,160, 55, 70]
band3 = [161, 165, 56, 75]
band4 = [166, 170, 57, 80]
band5 = [171, 175, 60, 88]
band6 = [176, 180, 60, 94]
band7 = [181, 185, 60, 100]
band8 = [186, 190, 63, 105]
band9 = [191, 195, 64, 110]
band10 = [196, 299, 65, 110]
# Put all the bands into a single array for easy use
bands = []
bands.append(band1)
bands.append(band2)
bands.append(band3)
bands.append(band4)
bands.append(band5)
bands.append(band6)
bands.append(band7)
bands.append(band8)
bands.append(band9)
bands.append(band10)
new_X = []
new_Y = []
for i inrange(0, 1000000):
index = randint(0, len(X) -1)
for band in bands:
if band[0] <= X[index] <= band[1]:
new_X.append(X[index])
new_Y.append(make_sample(band[2], band[3], mean, std))
plt.plot(new_X, new_Y, 'go',marker='^')
plt.plot(male.hgt, male.wgt, 'yo')
plt.plot(large_hgt, large_pred, 'go')
plt.plot(gen_height, prediction, 'ro')
plt.plot(old_min_hgt, old_min_wgt, 'bo')
plt.plot(old_max_hgt, old_max_wgt, 'bo')
plt.show()
Which gives us this!Banded Data There are still a million points, but some my be repeated. But, the general flow is far more similar to the real data which is perfect now for training a deep learning model.
Conclusion
From this blog, we saw how to use only two observations, the minimum and maximum, and how to create a fully synthetic dataset that can be used for deep learning.
The main idea when building a fully synthetic dataset is to ensure it is statistically and logically similar to that of the observed/real dataset. This gives the benefit of creating a large training dataset and then using the real data as a testing set. This can give very good results when creating a deep learning model as you won't have to train the model on the very limited (and precious) real data that can be very difficult to capture or collect.
This approach can be improved significantly, especially in the banding section. By adding a larger number of bands, smoothing out the lower and upper limits, and even using more complex algorithms like a random walk can improve the final results. But, this method still needs to be vetted before use in different models and/or real-world applications. The next step would be to model more independent variables, other phenomenons, and improve the generation steps.
References:
Heinz G, Peterson LJ, Johnson RW, Kerk CJ. 2003. Exploring Relationships in Body Dimensions. Journal of Statistics Education 11(2).
