The bias in question is falling off at a rate of
nis our sample size). So the bias issue loses what little gravity it ever may have ever had when working with big data. Most sources of noise will be falling off at a slower rate of
1/sqrt(n), so it is unlikely this bias is going to be the worst feature of your sample.
But let’s pretend the sample size correction indeed is an important point for a while.
Under the “no bias allowed” rubric: if it is so vitally important to bias-correct the variance estimate, would it not be equally critical to correct the standard deviation estimate?
The practical answer seems to be: no. The straightforward standard deviation estimate itself is biased (it has to be, as a consequence of Jensen’s inequality). And pretty much nobody cares, corrects it, or teaches how to correct it, as it just isn’t worth the trouble.
This is a good explanation of the topic as well as the reason people make these corrections so rarely.
Before, when describing the simple perceptron, I said that a result is calculated in a neuron, e.g. by summing up all the incoming data multiplied by weights. However, this has one big disadvantage: such an approach would only enable our neural net to learn linearrelationships between data. In order to be able to learn (you can also say approximate) any mathematical problem – no matter how complex – we use activation functions. Activation functions normalize the output of a neuron, e.g. to values between -1 and 1, (Tanh), 0 and 1 (Sigmoid) or by setting negative values to 0 (Rectified Linear Units, ReLU). In H2O we can choose between Tanh, Tanh with Dropout, Rectifier (default), Rectifier with Dropout, Maxout and Maxout with Dropout. Let’s choose Rectifier with Dropout. Dropout is used to improve the generalizability of neural nets by randomly setting a given proportion of nodes to 0. The dropout rate in H2O is specified with two arguments:
hidden_dropout_ratios, which per default sets 50% of hidden (more on that in a minute) nodes to 0. Here, I want to reduce that proportion to 20% but let’s talk about hidden layers and hidden nodes first. In addition to hidden dropout, H2O let’s us specify a dropout for the input layer with
input_dropout_ratio. This argument is deactivated by default and this is how we will leave it.
Read the whole thing and, if you understand German, check out the video as well.
DIM AND GLIMPSE
Next, we will run the dim function which displays the dimensions of the table. The output takes the form of row, column.
And then we run the glimpse function from the dplyr package. This will display a vertical preview of the dataset. It allows us to easily preview data type and sample data.
Spending some quality time doing EDA can save you in the long run, as it can help you get a feel for things like data quality, the distributions of variables, and completeness of data.
Since we are going to try algorithms like Logistic Regression, we will have to convert the categorical variables in the dataset into numeric variables. There are 2 ways we can do this.
- Category Indexing
- One-Hot Encoding
Click through for the code and explanation.
Specifically, let us assume that we wish to analyze traffic density for buses and coaches. The main thing we are interested in is the frequency of traffic across a particular route.
Let’s take an example. If buses cover 100 miles on a route that is 5 miles long within a certain timeframe, then the frequency will be greater than 100 miles covered on a route that is 10 miles long over the same time period.
Read on for an interesting example.
Notice only grouping columns and columns passed through an aggregating calculation (such as
max()) are passed through (the column
zis not in the result). Now because
yis a function of
xno substantial aggregation is going on, we call this situation a “pseudo aggregation” and we have taught this before. This is also why we made the seemingly strange choice of keeping the variable name
y(instead of picking a new name such as
max_y), we expect the
yvalues coming out to be the same as the one coming in- just with changes of length. Pseudo aggregation (using the projection
y[]) was also used in the solutions of the column indexing problem.
In this post, John calls the act of grouping functional dependencies (where we can determine the value of y based on the value of x, for any number of columns in y or x) pseudo-aggregation.
RF is based on decision trees. In machine learning decision trees are a technique for creating predictive models. They are called decision trees because the prediction follows several branches of “if… then…” decision splits – similar to the branches of a tree. If we imagine that we start with a sample, which we want to predict a class for, we would start at the bottom of a tree and travel up the trunk until we come to the first split-off branch. This split can be thought of as a feature in machine learning, let’s say it would be “age”; we would now make a decision about which branch to follow: “if our sample has an age bigger than 30, continue along the left branch, else continue along the right branch”. This we would do until we come to the next branch and repeat the same decision process until there are no more branches before us. This endpoint is called a leaf and in decision trees would represent the final result: a predicted class or value.
At each branch, the feature thresholds that best split the (remaining) samples locally is found. The most common metrics for defining the “best split” are gini impurity and information gain for classification tasks and variance reduction for regression.
Click through for more info and if you understand German, the video is good as well.
We leverage the power of HDP 3.0 from efficient storage (erasure coding), GPU pooling to containerized TensorFlow and Zeppelin to enable this use case. We will the save the details for a different blog (please see the video)- to summarize, as we trained the car on a track, we collected about 30K images with corresponding steering angle data. The training data was stored in a HDP 3.0 cluster and the TensorFlow model was trained using 6 GPU cards and then the model was deployed back on the car. The deep learning use case highlights the combined power of HDP 3.0.
Click through for more additions and demos.
This message will pop up, and it’s worth noting as it’s got some information in it that you might need to think about:
It’s worth noting that right now Microsoft r Client is lagging behind the current
Rversion, and is based on version 3.4 of
R, not 3.5. This will mean your default package libraries will not be shared between the installations if you are running
It’s using a snapshot of
MRANto source packages by default. 90% of the time it will operate just as you expect, but because it takes a ‘snapshot’ of packages, newer features and changes that have hit
CRANmay not be in the version of the package you are grabbing.
RevoScaleRand probably the
dplyrpackages will likely be installed for you already as default in Microsoft R Client. The other two you will probably have to install yourself.
Intel MKL will have scanned your system on install and attempted to work out how many cores your processor has. Here it’s identified 2 on my old Lenovo Yoga. This is where the speed boost will come from.
I had an old two-core Lenovo Yoga too, so this article really spoke to me.
For each of these images, I am running the
predict()function of Keras with the VGG16 model. Because I excluded the last layers of the model, this function will not actually return any class predictions as it would normally do; instead we will get the output of the last layer:
These, we can use as learned features (or abstractions) of the images. Running this part of the code takes several minutes, so I save the output to a RData file (because I samples randomly, the classes you see below might not be the same as in the
Read the whole thing.