Manifold learning and dimensionality reduction techniques are ubiquitous in science and engineering, but can be computationally expensive procedures when applied to large data sets or when similarities are expensive to compute. To date, little work has been done to investigate the tradeoff between computational resources and the quality of learned representations. We present both theoretical and experimental explorations of this question. In particular, we consider Laplacian eigenmaps embeddings based on a kernel matrix, and explore how the embeddings behave when this kernel matrix is corrupted by occlusion and noise. Our main theoretical result shows that under modest noise and occlusion assumptions, we can (with high probability) recover a good approximation to the Laplacian eigenmaps embedding based on the uncorrupted kernel matrix. Our results also show how regularization can aid this approximation. Experimentally, we explore the effects of noise and occlusion on Laplacian eigenmaps embeddings of two real-world data sets, one from speech processing and one from neuroscience, as well as a synthetic data set.

Most learning algorithms are not invariant to the scale of the function that is being approximated. We propose to adaptively normalize the targets used in learning. This is useful in value-based reinforcement learning, where the magnitude of appropriate value approximations can change over time when we update the policy of behavior. Our main motivation is prior work on learning to play Atari games, where the rewards were all clipped to a predetermined range. This clipping facilitates learning across many different games with a single learning algorithm, but a clipped reward function can result in qualitatively different behavior. Using the adaptive normalization we can remove this domain-specific heuristic without diminishing overall performance.

Our control model was a well established machine learning model using features that are known to work well. For text, the features are essentially normalized word counts (TF-IDF: term frequency / inverse document frequency vectors). For images, we use HOG features (histogram of oriented gradients). These features were fed into a logistic regression model for training and prediction. Our test model used custom collection; we fed data, trained a model, and made a prediction using transfer learning for text and image analysis under the covers.

Machine learning is, in essence, the process of applying algorithms to identify patterns in the data that correspond with the ground truth of that data. In our case, the ground truth is the reference values found in the GSL, and the patterns are the spectra for each sample. The regression model calculates a function to transform a spectrum into each of its reference values. For example, the presence of a significant peak in the spectrum could correspond with a high Potassium concentration. We also create regression models that allow us to predict how confident the predictions for a spectrum are.

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NIPS (which stands for "Neural Information Processing Systems") is an annual conference on machine learning and computational neuroscience, and papers presented there reveal what experts in the field are working on. Conveniently, you can find the data from the 2015 conference from Kaggle's NIPS 2015 Papers page. Let's load the data downloaded from Kaggle to the current folder. I also wrote a script nips2015_parse_html in order to parse the HTML file "accepted_papers.html" We can visualize which organization the authors of accepted papers belong to using graphs.

The fastest way to get good at applied machine learning is to practice on end-to-end projects. In this post you will discover how to work through a regression problem in Weka, end-to-end. Step-By-Step Regression Machine Learning Project Tutorial in Weka Photo by vagawi, some rights reserved. This tutorial will walk you through the key steps required to complete a machine learning project in Weka. Weka is the best platform for beginners getting started in applied machine learning.

This post is part of a series covering the exercises from Andrew Ng's machine learning class on Coursera. The original code, exercise text, and data files for this post are available here. We've now reached the last post in this series! It's been an interesting journey. Andrew's class was really well-done and translating it all to python has been a fun experience.

Before we build stats/machine learning models, it is a good practice to understand which predictors are significant and have an impact on the response variable. In this post we deal with a particular case when both your response and predictor are categorical variables. By the end of this you'd have gained an understanding of what predictive modelling is and what the significance and purpose of chi-square statistic is. We will go through a hypothetical case study to understand the math behind it. We will actually implement a chi-squared test in R and learn to interpret the results.

We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by maximal-linkage clusters. We work in the context of metric spaces with non-expansive maps, which is appropriate for modeling data processing which does not increase information content.