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Category: Machine Learning

Seven Essential Machine Learning Equations: A Cribsheet (Really, the Précis)

Seven Essential Machine Learning Equations: A Cribsheet (Really, the Précis)

Making Machine Learning As Simple As Possible Albert Einstein is credited with saying, Everything should be made as simple as possible, but not simpler. Machine learning is not simple. In fact, once you get beyond the simple “building blocks” approach of stacking things higher and deeper (sometimes made all too easy with advanced deep learning packages), you are in the midst of some complex stuff. However, it does not need to be more complex than it has to be.  …

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A Tale of Two Probabilities

A Tale of Two Probabilities

Probabilities: Statistical Mechanics and Bayesian:   Machine learning fuses several different lines of thought, including statistical mechanics, Bayesian probability theory, and neural networks. There are two different ways of thinking about probability in machine learning; one comes from statistical mechanics, and the other from Bayesian logic. Both are important. They are also very different. While these two different ways of thinking about probability are usually very separate, they come together in some of the more advanced machine learning topics, such…

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Labor Day Reading and Academic Year Kick-Off

Labor Day Reading and Academic Year Kick-Off

Deep Learning / Machine Learning Reading and Study Guide:   Several of you have been asking for guided reading lists. This makes sense.   Your Starting Point for Neural Networks, Deep Learning, and Machine Learning   Your study program (reading and code) depends on where you are. Starting out (High-grass country; St. Louis to Alcove Springs): Basic neural networks and deep learning; architecture for common networks, such as CNNs (convolutional neural networks); learning rules and architecture design. Well on the…

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The Statistical Mechanics Underpinnings of Machine Learning

The Statistical Mechanics Underpinnings of Machine Learning

Machine Learning Is Different Now:   Actually, machine learning is a continuation of what it always has been, which is deeply rooted in statistical physics (statistical mechanics). It’s just that there’s a culmination of insights that are now a very substantive body of work, with more theoretical rigor behind them than most of us know.     A Lesson from Mom: It takes a lot of time to learn a new discipline. This is something that I learned from my…

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Seven Statistical Mechanics / Bayesian Equations That You Need to Know

Seven Statistical Mechanics / Bayesian Equations That You Need to Know

Essential Statistical Mechanics for Deep Learning   If you’re self-studying machine learning, and feel that statistical mechanics is suddenly showing up more than it used to, you’re not alone. Within the past couple of years, statistical mechanics (statistical thermodynamics) has become a more integral topic, along with the Kullback-Leibler divergence measure and several inference methods for machine learning, including the expectation maximization (EM) algorithm along with variational Bayes.     Statistical mechanics has always played a strong role in machine…

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Deep Learning: The Fast Evolution of Artificial Intelligence

Deep Learning: The Fast Evolution of Artificial Intelligence

Just one of the slides from a presentation that I’m working up for an upcoming online presentation at Northwestern University, but it tells the story. Just one more thought: here’s the rapid pace of evolution within just the image analysis realm of AI, largely due to multiple layers (sometimes, many, many, MANY multiple layers) of networks, a good fraction of which are Convolutional Neural Networks, or CNNs.

Neural Networks and Python Code: Be Careful with the Array Indices!

Neural Networks and Python Code: Be Careful with the Array Indices!

Our Special Topics class on Deep Learning (Northwestern University, Master of Science in Predictive Analytics program, Winter, 2017) starts off with very basic neural networks: the backpropagation learning method applied to the classic X-OR problem. I’m writing Python code to go with this class, and the result by the end of the quarter should be five-to-six solid pieces of code, involving either the backpropagation or Boltzmann machine learning algorithm, with various network configurations. The following figure shows the dependence of…

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Deep Learning: The First Layer

Deep Learning: The First Layer

It’s been something of a challenging week. We’ve kicked off our new PREDICT 490 Special Topics Course in Deep Learning at Northwestern University. I’ve got a full house; there’s been a waiting list since Thanksgiving, and everyone is acutely aware of the business climate surrounding deep learning. However (and I’m not terribly surprised here), most people who want to learn Deep Learning (DL) really don’t have a solid foundation in neural networks just yet. Thus, what we’re really doing is…

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Getting Started in Deep Learning

Getting Started in Deep Learning

It’s been a lovely Christmas day. More social than any that I can remember, for a very long time. (Wonderful morning visit with my next-door neighbor. Great mid-day party. A sweet restorative nap afterwards.) And now, the thoughts that have been buzzing through and around my head for the past 48 hours — how to get started with deep learning. Of course there are all sorts of entry points. Historical, functional, mathematical… But what came to me, over these past…

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Approximate Bayesian Inference

Approximate Bayesian Inference

Variational Free Energy I spent some time trying to figure out the derivation for the variational free energy, as expressed in some of Friston’s papers (see citations below). While I made an intuitive justification, I just found this derivation (Kokkinos; see the reference and link below): Other discussions about variational free energy: Whereas maximum a posteriori methods optimize a point estimate of the parameters, in ensemble learning an ensemble is optimized, so that it approximates the entire posterior probability distribution…

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