In this post we’ll improve our training algorithm from the previous post. When we’re done we’ll be able to achieve 98% precision on the MNIST data set, after just 9 epochs of training—which only takes about 30 seconds to run on my laptop. For comparison, last time we only achieved 92% precision after 2,000 epochs of training, which took over an hour! The main driver in this improvement is just switching from batch gradient descent to mini-batch gradient descent.... Read more

In this post we’re going to build a neural network from scratch. We’ll train it to recognize hand-written digits, using the famous MNIST data set. We’ll use just basic Python with NumPy to build our network (no high-level stuff like Keras or TensorFlow). We will dip into scikit-learn, but only to get the MNIST data and to assess our model once its built. We’ll start with the simplest possible “network”: a single node that recognizes just the digit 0.... Read more

Location: University of Toronto Dates: June 12–14, 2018 Keynote Speakers: Lara Buchak and Mike Titelbaum Submission Deadline: February 12, 2018 Authors Notified: March 31, 2018 We are pleased to invite papers in formal epistemology, broadly construed to include related areas of philosophy as well as cognate disciplines like statistics, psychology, economics, computer science, and mathematics. Submissions should be: prepared for anonymous review, no more than 6,000 words, accompanied by an abstract of up to 300 words, and in PDF format.... Read more

This post is coauthored with Johanna Thoma and cross-posted at Choice & Inference. Accompanying Mathematica code is available on GitHub. Lara Buchak’s Risk & Rationality advertises REU theory as able to recover the modal preferences in the Allais paradox. In our commentary we challenged this claim. We pointed out that REU theory is strictly “grand-world”, and in the grand-world setting it actually struggles with the Allais preferences. To demonstrate, we constructed a grand-world model of the Allais problem.... Read more

One of my favourite probability puzzles to teach is a close cousin of the Monty Hall problem. Originally from a 1965 book by Frederick Mosteller,1 here’s my formulation: Three prisoners, A, B, and C, are condemned to die in the morning. But the king decides in the night to pardon one of them. He makes his choice at random and communicates it to the guard, who is sworn to secrecy.... Read more

In our last two posts we established two key facts: The set of possible probability assignments is convex. Convex sets are “obtuse”. Given a point outside a convex set, there’s a point inside that forms a right-or-obtuse angle with any third point in the set. Today we’re putting them together to get the central result of the accuracy framework, the Brier dominance theorem. We’ll show that a non-probabilistic credence assignment is always “Brier dominated” by some probabilistic one.... Read more

Update: editors at CJP and Phil Quarterly have kindly shared some important, additional information. See the edit below for details. A new paper on the representation of women in philosophy journals prompted some debate in the philosophy blogosphere last week. The paper found women to be underrepresented across a range of prominent journals, yet overrepresented in the two journals studied where review was non-anonymous. Commenters over at Daily Nous complained about the lack of base-rate data.... Read more

Last time we saw that the set of probability assignments is convex. Today we’re going to show that convex sets have a special sort of “obtuse” relationship with outsiders. Given a point outside a convex set, there is always a point in the set that forms a right-or-obtuse angle with it. Recall our 2D diagram from the first post. The convex set of interest here is the diagonal line segment from $(0,1)$ to $(1,0)$:... Read more

In this and the next two posts we’ll establish the central theorem of the accuracy framework. We’ll show that the laws of probability are specially suited to the pursuit of accuracy, measured in Brier distance. We showed this for cases with two possible outcomes, like a coin toss, way back in the first post of this series. A simple, two-dimensional diagram was all we really needed for that argument. To see how the same idea extends to any number of dimensions, we need to generalize the key ingredients of that reasoning to $n$ dimensions.... Read more

Starting in July, philosophy’s two most prestigious journals won’t reject submitted papers anymore. Instead they’ll “grade” every submission, assigning a rating on the familiar letter-grade scale (A+, A, A-, B+, B, B-, etc.). They will, in effect, become ratings agencies. They’ll still publish papers. Those rated A- or higher can be published in the journal, if the authors want. Or they can seek another venue, if they think they can do better.... Read more