Simplifying ML: Recommender Systems - Part 7

In this age of Amazon, Netflix and App stores where products, movies and apps are purchased online the method of up-selling and cross-selling online is through the use of recommender based systems.

When you go to site like Amazon/Flipkart or purchase apps on App store/Google Play we often see things like “People who bought this book/app also bought X, Y, Z”. These recommendations are the recommender system algorithms in action.

Recently, Netflix ran a competition in which users had to come with the best algorithm to recommend films that a user would also like. The prize money for this was of the order of $1 million. That’s how critical recommender systems are to organizations of today where most of the transactions happen on the web.

Typically users are asked to give a rating of 1 to 5 with 1 being the lowest and 5 being the highest.  So for example if we had classics like Moby Dick, Great Expectations and current best sellers like The Client, The da Vinci Code and a Science Fiction like 2001- A Space Odyssey we can expect that different people will rate the books differently. Obviously not everybody would have read every book in the list and some elements would be blank.

Recommender Systems are based on machine learning algorithms. The goal of these algorithms is to predict what score any user would give to books they did not rate. In other words what would be rating the buyers would give for books or apps they did not buy. So if the algorithm predicts a high rating then we could recommend that the user would also ‘like’ them. Or we could give recommendations of books/apps bought by users who bought the books/apps bought by this user.

The notation is

n_u = Number of users

n_b = Number of books

r^(i,j) = Boolean whether user j rated a book i

y^(i,j) = The rating user j gave book i

m_j  = The number of books that user j rated

Content based recommendation

In a typical content based recommendation algorithm we assume that we have data about some items we want to recommend rating for e.g. books/products/apps.  In the example for books bought in an online bookstore we assume some features in our case ‘classic’, “fiction” etc

So each book has its own feature vector where x¹ is the feature vector of the first book x²  feature vector of the 2nd book and so on

This can be done through linear regression by minimizing the cost function of the sum of squared errors from the predicted value

So for a parameter vector Ɵ^jand a feature vector xⁱ the recommender system will try to predict the rating that a user j will give a book i.

This can be written as

Number of stars (rating) = (θ^j) ^T xⁱ

This reduces to the minimization problem over all θ^j for r=1

min 1/2m Σ  ((θj)^T xⁱ  - y ^i,j)²

θ^j                  i:r=1

Adding the regularization term this becomes

min 1/2m Σ((θ^j)^T xⁱ  - y ^i,j)²  + λ/2m(Σ θ^j)²

θ^j                  i:r=1

The recommender algorithm in essence tries to learn parameters θ^j for a set of features of xⁱ the chosen system for e.g.  books in this case.

The recommender tries to learn the parameters for all the users

min 1/2m Σ Σ((θ^j)^T xⁱ  - y ^i,j)²  + λ/2m(Σ Σ θ^j)²

θ¹...θⁿ                i:r=1

The minimization is performed by gradient descent as

Θ^j _k:= Θ^j_k – α (Σ((θ^j)^T xⁱ  - y ^i,j)xⁱ + λ Θ^j _k

Recommender systems tries to learn the parameters for a set of chosen features over all users. Based on the learnt paramaters it then tries to predict the rating the user would give to books/apps that he is yet to purchase and push up those apps for which the user is likely to give a high rating based on the given set of ratings.

Recommender systems contribute substantially to the revenues of e-commerce sites like Amazon, Flipkart, Netflix etc

Note: This post, line previous posts on Machine Learning,  is based on the Coursera course on Machine Learning by Professor Andrew Ng
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Perils and pitfalls of Big Data

Big Data is hurtling towards us in a big way. It is already in the news and the blip seems to getting bigger. Big Data will soon become the key driver for almost any kind of decision that is to be made in manufacturing, retail, finance all the way to astronomy, oceanography etc. The common aspect of all industries and areas is that data is generated in the order of several petabytes to exabytes. Big Data is the technique to analyze such large volumes of data.

Big Data represents the technique to handle the huge deluge of data that is already becoming enmeshed in our lives. Multiple disparate, varied streams of data (text. tweets, click streams, html) flow through with tremendous volume & velocity. The key aspects of data in the world are the volume, variety and the velocity. It is never ending and never seems to stop. How do we handle this deluge? How do we make sense of this data is what Big Data is all about.

Big Data provides algorithms to find patterns, determine trends or classify data depending on the features provided. It is supposed to enable the decision makes to make key decisions based on the answers the algorithms spew forth.

Big Data is also complicated by the fact that data comes is multiple forms from click streams, tweets, html, texts, CSVs, structured and non –structured data.

The ability to detect patterns, determine trends, classify, identify outliers is no easy task

In this post I try to take a philosophical look at Big Data and ask whether it can really help us. Will it help or will take is on wild goose chase? Can we trust the results?

Big Data depends on algorithms to make sense of data. Big Data deals with data that is in the order of Petabytes to Exabytes. At this scale with multiple features our cognitive abilities are of no use. We must rely on machines and algorithms to make sense of these large amounts of data. Our mind can handle a few hundred data points and at most 3 dimensions. Beyond that the data  can hardly make any sense.

Data by itself, in the absence of features & algorithms, is indistinguishable from noise. It is data science that makes sense of data. Data science separates the signal from the noise.

It is the algorithms that try to determine the best fit for a given set of data. But how reliable are the results. For example let us take the following case

An unsupervised learning algorithm for the above data points could try to separate the data into 2 sets. Clearly this is one way but what is more appropriate is that we have 2 shapes, the circle & the rectangle. A machine algorithm would try to work based on the features that we choose. Are we in a position to decide whether the answer the algorithm gives us is correct? We have no way of knowing because the amount of data is beyond our cognitive capabilities,

In other words, Big Data is full of perils and pitfalls.

When we let the machine to analyze on our behalf the possibility of coming to a wrong conclusion is fairly high.  This coupled with the fact that we are sometimes led to erroneous judgments, as discussed below, the problem is further compounded.

In his book “Thinking fast, thinking slow” Daniel Kahneman discusses several situations where our mind falls into the traps of lazy thinking. We come to wrong conclusions. Also our minds tend to detect patterns in data where there are none. Sometimes according to Kahneman ‘randomness appears as regularity or a tendency to cluster’. Also he says ‘the tendency to see patterns in randomness is overwhelming’. We could argue that in Big Data it is the algorithm that is determining the pattern we could be tricked into coming to false conclusions. Sometimes the human mind sees causality where there is none. Occasionally we fail to see the obvious.

In the ‘famous gorilla experiment’ the researchers tried to assess selective attention. The participants are asked to count the number of passes those in white t-shirts make. Surprisingly a large number of the participants were complete oblivious a gorilla that appears midway in the video. When we, as human fail to see such large objects, can we expect the machine to accurately identify patterns and perform accurate classifications?

There are techniques that help in determining false positives for e.g. the Bonferroni correction. Simply put the Bonferroni correction tries to determine the possibility of getting at least 1 significant result when one is testing 20 hypothesis simultaneously. If we want to test 20 hypotheses with the significance of 0.05 then the probability of at least 1 significant result is

P(at least one significant result) = 1 - P(no significant results)

= 1 - (1 - 0:05)^20

= 0.64

So, with 20 tests being considered, we have a 64% chance of observing at least one significant result, even if all of the tests are actually not significant. This would be a false positive.

Given that our ability to come to significant conclusions depends largely on being able to choose appropriate features, we must also be able to maneuver between false negatives and false positives. In addition we must also take into account the fallibility of the human mind.

Clearly, Big Data is the future! However with Big Data we are really on treacherous, slippery ground!