## Broyden’s Method in Python

In a previous post we looked at root-finding methods for single variable equations. In this post we’ll look at the expansion of Quasi-Newton methods to the multivariable case and look at one of the more widely-used algorithms today: Broyden’s Method.

## Root-Finding Algorithms Tutorial in Python: Line Search, Bisection, Secant, Newton-Raphson, Inverse Quadratic Interpolation, Brent’s Method

Motivation

How do you find the roots of a continuous polynomial function? Well, if we want to find the roots of something like:

$f(x) = x^2 + 3x - 4$

## DropConnect Implementation in Python and TensorFlow

I wouldn’t expect DropConnect to appear in TensorFlow, Keras, or Theano since, as far as I know, it’s used pretty rarely and doesn’t seem as well-studied or demonstrably more useful than its cousin, Dropout. However, there don’t seem to be any implementations out there, so I’ll provide a few ways of doing so. Continue reading “DropConnect Implementation in Python and TensorFlow”

## MLE, MAP, and Naive Bayes

Suppose we are given a dataset $X$ of outcomes from some distribution parameterized by $\Theta$. How do we estimate $\Theta$?

For example, given a bent coin and a series of heads and tails outcomes from that coin, how can we estimate the probability of the coin landing heads? Continue reading “MLE, MAP, and Naive Bayes”

## Shallow Parsing for Entity Recognition with NLTK and Machine Learning

Getting Useful Information Out of Unstructured Text

Let’s say that you’re interested in performing a basic analysis of the US M&A market over the last five years. You don’t have access to a database of transactions and don’t have access to tombstones (public advertisements announcing the minimal details of a closed deal, e.g. ABC acquires XYZ for \$500mm). What you do have is access to is a large corpus of financial news articles that contain within them – somewhere – the basic transactional details of M&A deals.

What you need to do is design a system that takes in this large database and outputs clean fields containing M&A transaction details. In other words, map an excerpt like this: Continue reading “Shallow Parsing for Entity Recognition with NLTK and Machine Learning”

## Multi-label Classification: A Guided Tour

Introduction

I recently undertook some work that looked at tagging academic papers with one or more labels based on a training set.

A preliminary look through the data revealed about 8000 examples, 2750 features, and…650 labels. For clarification, that’s 2750 sparse binary features (keyword indices for the articles), and 650 labels, not classes. Label cardinality (average number of labels per example) is about 2, with the majority of labels only occurring a few times in the dataset…doesn’t look good, does it? Nevertheless, more data wasn’t available and label reduction wasn’t on the table yet, so I spent a good amount of time in the corners of academia looking at multi-label work.

## Trump Tweet Analysis

This project stems from two overarching questions:

#### Which emotions do politicians most frequently appeal to?

I recently saw a BuzzFeed presentation on, among other things, the virality of BuzzFeed content. A big part of their business relies on understanding what kind of content goes viral and why, so their data science team understandably spends a lot of time not only looking at how a piece of content becomes widely popular, but also looking at the distribution of content types in their most popular pieces of content. Continue reading “Trump Tweet Analysis”