# Programming Language Classifier

In this post, I’ll explain some of the details that went into http://langclass.kevinlui.org/. A fun thing I did was feature importance recovery after feature hashing. I’ll explain that at the end.

# Data source

The data was retrieve from the Rosetta Code Project using this git repo: https://github.com/acmeism/RosettaCodeData. The features are code snippets and the labels are programming languages.

# Tokenization

We consider 2 different tokenizers.

character-level tokenization.

`print('Hello World') ==> ['p', 'r', 'i', 'n' 't', '(', ...]`

split on non-alphanumerical.

`print('Hello World') ==> ['print', '(', 'Hello', 'World', ')']`

# Vectorization

After tokenizing, we consider consider 1-grams followed by feature hashing modulo 4098. We also do the same with 2-grams.

# Classifier

We use lightgbm with default parameters. There’s a lot of tuning to be done but that wasn’t my main interest so I’m putting it off.

# Feature Importance

A fun thing I did was feature importance extraction despite feature hashing. After training a tree-based model on feature-hashed inputs, you can normally only determine the feature importance of the hash values. For example, you might discover that the hash 123 has high importance. But this does not tell you which one of our original tokens has high importance. You can determine which tokens hashes to 123 but it could be the case that many tokens share the same hash value. In the next section, we share an idea for recovering the feature importance of the original tokens.

The top features for character-level 2-grams are:

```
[';\n', ')\n', ' (', ', ', ' =', '= ', 't(', 't ', 'in', '# ']
```

The top features for 1-grams where we split on non-alphanumericals are:

```
[';', '=', '.', ':', 'print', ',', '"', '#', ')', '-']
```

The most importance feature in both cases contains a semi-colon. This is unsurprising since some programming languages seldomly use semi-colons (for example, Python) while some programming languages use semi-colons extensively (for example, C).

# Mathematical Heuristic

This technique is mainly inspired by bloom-filters. For ease of exposition, we’ll focus on the character-level 2-grams case. Let $X$ be the space of character-level 2-grams, $Y$ be the hashed space, and $H_1, H_2, H_3:X \to Y$ be 3 different hash functions. In our implementation, we take $H_i$ to be the murmur3 hash with seed $i$.

For $x\in X$, let $f_x$ be the feature importance of $x$ if we were to train our model using unhashed features. For $y\in Y$ and $t\in \{1,2,3\}$, let $g_y ^t$ be the feature importance of $y$ using the hash function $H_t$. For our heuristic, we assume that $g_y ^t$ is approximately $\sum_{x\in H_t ^{-1}(y)} f_x$.

Our model is trained on the hashed space so we have access to $g_y ^t$. Our goal is to understand $f_x$. We can of course approximate the solution to a massive linear system so try to recover $f_x$ but what we’re really interested is a ranking of $f_x$. So do this, we’ll use the geometric-mean of the hashed values. In particular, let $F_x = (\prod_{t=1} ^3 g_{H_t(x)} ^t)^{1 /3}$. Then we can show that if $f_x > f_y$, then $\mathbb{E}(F_x)>\mathbb{E}(F_y)$.