Friday, 5 August 2016

Image recognition tutorial in R using deep convolutional neural networks (MXNet package)

This is a detailed tutorial on image recognition in R using a deep convolutional neural network provided by the MXNet package. After a short post I wrote some times ago I received a lot of requests and emails for a much more detailed explanation, therefore I decided to write this tutorial. This post will show a reproducible example on how to get 97.5% accuracy score on a faces recognition task in R.


Plain vanilla recurrent neural networks in R: waves prediction

While continuing my study of neural networks and deep learning, I inevitably meet up with recurrent neural networks.

Recurrent neural networks (RNN) are a particular kind of neural networks usually very good at predicting sequences due to their inner working. If your task is to predict a sequence or a periodic signal, then using a RNN might be a good starting point. Plain vanilla RNN work fine but they have a little problem when trying to “keep in memory” events occured, say for instance, more than 20 steps back. The solution to this problem has been addressed with the development of a model called LSTM network. As far as I know, LSTM should usually be preferred to a plain vanilla RNN when possible as it yields better results.

Monday, 25 July 2016

Image recognition in R using convolutional neural networks with the MXNet package

Among R deep learning packages, MXNet is my favourite one. Why you may ask? Well I can’t really say why this time. It feels relatively simple, maybe because at first sight its workflow looks similar to the one used by Keras, maybe because it was my first package for deep learning in R or maybe because it works very good with little effort, who knows.

MXNet is not available on CRAN but it can be easily installed either by using precompiled binaries or by building the package from scratch. I decided to install the GPU version but for some reason my GPU did not want to collaborate so I installed the CPU one that should be fine for what I plan on doing.


As a first experiment with this package, I decided to try and complete some image recognition tasks. However, the first big problem is where to find images to work on, while at the same time not using the same old boring datasets. ImageNet is the correct answer! It provides a collection of URLs to images publicly available that can be downloaded easily using a simple R or Python script.

Sunday, 24 July 2016

Fluid Dynamics: Pressure Drop Modelling [heavily revised]

Some time ago I uploaded a short script on modelling pressure drop in a circular diameter pipe. While at the time I felt I did a good job, I knew there sure was room for improvement. After having attended a (very tough) course on fluid dynamics and applied physics, I feel a lot more confident on this topic and therefore I would like to share a little model I built for a project I am working on.


Tuesday, 29 March 2016

How to fit a copula model in R [heavily revised]. Part 2: fitting the copula

Here I am again with part 2. If you would like to read part 1 of this short tutorial on copulas, please click here.

In this second post I am going to select a copula model, fit it to a test dataset, evaluate the fitting and generate random observations from the fitted multivariate distribution. Furthermore I am going to show how to measure correlation using Spearman's Rho and Kendall's Tau. In order to run the code in this post you need the following packages: copula and VineCopula.

The dataset

For this example I am going to use a test dataset. You can download it from this link. This test dataset contains two variables, x and y, characterized by a strong left tail correlation.

By visually inspecting the plot of x versus y you can easily notice that low values of x tends to be highly correlated with low values of y.


Sunday, 13 March 2016

How to fit a copula model in R [heavily revised]. Part 1: basic tools

More than a year ago I wrote a short post on how to fit a copula model in R. The post showed how to make a very raw and basic fitting of a test dataset to a two dimensional normal copula (or a gaussian copula if you wish) using the copula package. The content of the post was not much, but that was a big part of what I knew about how to use copulas in R at that time and there was not much documentation available other than the official copula package documentation which is quite technical in my opinion (as it should be) and may not be that easy for a beginner copula user.

Monday, 15 February 2016

Simulating a mass attached to a spring with control theory

Control system theory is very useful when it comes to simulate physical systems and their behaviour.
Suppose you have a mass attached to a spring on an horizontal flat surface. The force diagram associated with this physical system can be sketched as follows:


By analysing the force diagram, you can actually see that on the x axis the only forces acting on the mass are the elastic force (Fe), the friction (Fr) due to the air resistance and the external force applied to the mass (u). On the y axis the normal force and the force of gravity balance out, therefore there is no motion.

Sunday, 14 February 2016

Solving a circuit with a mutual inductor using LTspice

Mutual inductors can be a lot of fun, and sometimes a bit of an headache if you mess something up or represent them in a complicated way. Take for instance the following circuit designed with Circuit Lab a great online circuit design and simulator tool


This is one of the first excercises we were taught in our circuit class. As you can probably see, the circuit is composed by two current sources with different frequency, some resistors and a mutual inductor. The aim of the analysis is to find out the total power consumed by the resistors. Let's analyse each problem carefully before proceeding.

Tuesday, 22 December 2015

Step response of a RLC series circuit

Today I am going to make a brief description of the step response of a RLC series circuit. This is the schematic made with LTspice

Immagine 1

As you can see the components used are a resistor, an inductor and a capacitor connected in series. By applying Kirchhoff voltage law we obtain the following equation

$$u(t) = R x(t) + L\frac{dx(t)}{dt} + \frac{1}{C} \int x(t)dt $$

Monday, 21 December 2015

Three-phase symmetric perfectly balanced system LTspice simulation

A symmetric, three-phase and perfectly balanced system can be easily modelled either by pen and paper with the use of phasors or using LTspice which is faster. In case you would like to try I suggest to first try the pen and paper way and then check the results on the simulator. A basic example of such system would be the following:

Immagine 1

Tuesday, 8 December 2015

How to simulate a simple high pass filters on LTspice

Here I am again after a long break!

During my last engineering class I learnt about the frequency response of a system and how this thing can be applied to solve simple problems. But the crucial question from most of us was the following: how would you build such filters, and perhaps more importantly, how would you tune them?

In principle, you could build a simple filter using nothing more than a resistor and a capacitor and, as you might have guessed, LTspice once again comes at rescuing us from our wandering around.

Let’s say we would like to build a simple high pass filter. Then we could try building the following circuit

Monday, 28 September 2015

Selecting the number of neurons in the hidden layer of a neural network

Recently I wrote a post for DataScience+ (which by the way is a great website for learning about R) explaining how to fit a neural network in R using the neuralnet package, however I glossed over the “how to choose the number of neurons in the hidden layer” part. The glossing over is mainly due to the fact that there is no fixed rule or suggested “best” rule for this task but the mainstream approach (as far as I know) is mostly a trial and error process starting from a set of rules of thumb and a heavy cross validating attitude.

Tuesday, 15 September 2015

Predicting creditability using logistic regression in R: cross validating the classifier (part 2)

Now that we fitted the classifier and run some preliminary tests, in order to get a grasp at how our model is doing when predicting creditability we need to run some cross validation methods.
Cross validation is a model evaluation method that does not use conventional fitting measures (such as R^2 of linear regression) when trying to evaluate the model. Cross validation is focused on the predictive ability of the model. The process it follows is the following: the dataset is splitted in a training and testing set, the model is trained on the testing set and tested on the test set.

Note that running this process one time gives you a somewhat unreliable estimate of the performance of your model since this estimate usually has a non-neglectable variance.

Wednesday, 2 September 2015

Predicting creditability using logistic regression in R (part 1)

As I said in the previous post, this summer I’ve been learning some of the most popular machine learning algorithms and trying to apply what I’ve learned to real world scenarios. The German Credit dataset provided by the UCI Machine Learning Repository is another great example of application.

The German Credit dataset contains 1000 samples of applicants asking for some kind of loan and the creditability (either good or bad)  alongside with 20 features that are believed to be relevant in predicting creditability. Some examples are: the duration of the loan, the amount, the age of the applicant, the sex, and so on. Note that the dataset contains both categorical and quantitative features.
This is a classical example of a binary classification task, where our goal is essentially to build a model that can improve the selection process of the applicants.

Monday, 24 August 2015

RandomForestClassifier on the cars dataset ML

Since the beginning of this summer I have been practicing a lot with Scikit-learn to improve my knowledge of Machine Learning both on theory and practice. Last week I also tried to tackle some of the Kaggle competitions although they are really tough if you wish to get into the top 50 best scores. Perhaps I will post something about the experience in the future.

Scikit-learn is a (almost) ready to use package for Machine Learning in Python. It is so very user friendly and in some cases not that much coding around is needed to achieve interesting results such as in the case of the cars dataset.

The cars dataset, from the UCI Machine Learning Repository, is a collection of about 1700 entries of cars each with 6 features that can be easily recognized by the name (buying, maint, doors, persons, lug_boot, safety). Check the dataset description for more detailed information. The feature to be predicted is “class” and the possible values are unacc,acc,good,v-good. Most of the features are categorical, therefore they need to be encoded into numbers. Pandas is great for quick features encoding.