Abstract We present PAC-Bayesian bounds for the generalisation error of the K-nearest-neighbour classifier (K-NN). This is achieved by casting the K-NN classifier into a kernel space framework in the limit of vanishing kernel bandwidth. We establish a relation between prior measures over the coefficients in the kernel expansion and the induced measure on the weight vectors in kernel space. Defining a sparse prior over the coefficients allows the application of a PAC-Bayesian folk theorem that leads to a generalisation bound that is a function of the number of redundant training examples: those that can be left out without changing the solution. The presented bound requires to quantify a prior belief in the sparseness of the solution and is evaluated after learning when the actual redundancy level is known. Even for small sample size (m ~ 100) the bound gives non-trivial results when both the expected sparseness and the actual redundancy are high.

Prediction rule ensembles (PRE) provide interpretable prediction models with relatively high accuracy.PRE obtain a large set of decision rules from a (boosted) decision tree ensemble, and achieves sparsitythrough application of Lasso-penalized regression. This article examines the use of surrogate modelsto improve performance of PRE, wherein the Lasso regression is trained with the help of a massivedataset generated by the (boosted) decision tree ensemble. This use of model-based data generationmay improve the stability and consistency of the Lasso step, thus leading to improved overallperformance. We propose two surrogacy approaches, and evaluate them on simulated and existingdatasets, in terms of sparsity and predictive accuracy. The results indicate that the use of surrogacymodels can substantially improve the sparsity of PRE, while retaining predictive accuracy, especiallythrough the use of a nested surrogacy approach.

Motivated by the problem of learning when the number of training samples is small, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is the ability to incorporate domain knowledge of invariances, e.g., translational invariance of images. Kernels based on the \textit{minimum} distance over a group of transformations, which corresponds to defining similarity as the \textit{best} over the possible transformations, are not generally positive definite. Perhaps it is for this reason that they have neither previously been experimentally tested for their performance nor studied theoretically. Instead, previous attempts have employed kernels based on the \textit{average} distance over a group of transformations, which are trivially positive definite, but which generally yield both poor margins as well as poor performance, as we show. We address this lacuna and show that positive definiteness indeed holds \textit{with high probability} for kernels based on the minimum distance in the small training sample set regime of interest, and that they do yield the best results in that regime. Another important property of CNNs is their ability to incorporate local features at multiple spatial scales, e.g., through max pooling. A third important property is their ability to provide the benefits of composition through the architecture of multiple layers. We show how these additional properties can also be embedded into SVMs. We verify through experiments on widely available image sets that the resulting SVMs do provide superior accuracy in comparison to well-established deep neural network (DNN) benchmarks for small sample sizes.

This document is intended to help those with a basic knowledge of machine learning get the benefit of Google's best practices in machine learning. It presents a style for machine learning, similar to the Google C Style Guide and other popular guides to practical programming. If you have taken a class in machine learning, or built or worked on a machine -learned model, then you have the necessary background to read this document. Most of the problems you will face are, in fact, engineering problems. Even with all the resources of a great machine learning expert, most of the gains come from great features, not great machine learning algorithms. This approach will work well for a long period of time. Diverge from this approach only when there are no more simple tricks to get you any farther. Adding complexity slows future releases. Once you've exhausted the simple tricks, cutting -edge machine learning might indeed be in your future. See the section on Phase III machine learning projects. Machine learning is cool, but it requires data. Theoretically, you can take data from a different problem and then tweak the model for a new product, but this will likely underperform basic heuristics. If you think that machine learning will give you a 100% boost, then a heuristic will get you 50% of the way there. For instance, if you are ranking apps in an app marketplace, you could use the install rate or number of installs as heuristics. If you are detecting spam, filter out publishers that have sent spam before. Don't be afraid to use human editing either. If you need to rank contacts, rank the most recently used highest (or even rank alphabetically). If machine learning is not absolutely required for your product, don't use it until you have data. Before formalizing what your machine learning system will do, track as much as possible in your current system.

There won't be any business insights if the data quality is poor. When preparing data, I often go through many different approaches to reach a level of quality of data that can provide accurate results. In this article, I describe how unsupervised ML can help in data preparation for machine learning projects and how it helps to get more accurate business insights. For accurate predictions, the data must not only be properly labeled, de-deputed, broad, consistent, etc. The point is that the machine learning model should process the "right" data.

In this article, we'll learn about XGBoost, its background, its widely accepted usage in competitions such as Kaggle's and help you build an intuitive understanding of it by diving into the foundation of this algorithm. XGBoost is an algorithm that is highly flexible, portable, and efficient which is based on a decision tree for ensemble learning for Machine Learning that uses the distributed gradient boosting framework. Machine Learning algorithms are implemented with XGBoost under the Gradient boosting framework. XGBoost is capable of solving data science problems accurately in a short duration with its parallel tree boosting which is also called Gradient Boosting Machine (GBM), Gradient Boosting Decision Trees (GBDT). It is extremely portable and cross-platform enabled such that the very same code can be run on the different major distributed environments such as Hadoop, MPI, and SGE and enables solving problems with well over billions of examples.

Mastering unsupervised learning opens up a broad range of avenues for a data scientist. There is so much scope in the vast expanse of unsupervised learning and yet a lot of beginners in machine learning tend to shy away from it. In fact, I'm sure most newcomers will stick to basic clustering algorithms like K-Means clustering and hierarchical clustering. While there's nothing wrong with that approach, it does limit what you can do when faced with clustering projects. And why limit yourself when you can expand your learning, knowledge, and skillset by learning the powerful DBSCAN clustering algorithm?

The coronavirus disease (COVID-19) has rapidly spread throughout the world and while pregnant women present the same adverse outcome rates, they are underrepresented in clinical research. We collected clinical data of 155 test-positive COVID-19 pregnant women at Stony Brook University Hospital. Many of these collected data are of multivariate categorical type, where the number of possible outcomes grows exponentially as the dimension of data increases. We modeled the data within the unsupervised Bayesian framework and mapped them into a lower-dimensional space using latent Gaussian processes. The latent features in the lower dimensional space were further used for predicting if a pregnant woman would be admitted to a hospital due to COVID-19 or would remain with mild symptoms. We compared the prediction accuracy with the dummy/one-hot encoding of categorical data and found that the latent Gaussian process had better accuracy.

Traditionally, fault detection and isolation community has used system dynamic equations to generate diagnosers and to analyze detectability and isolability of the dynamic systems. Model-based fault detection and isolation methods use system model to generate a set of residuals as the bases for fault detection and isolation. However, in many complex systems it is not feasible to develop highly accurate models for the systems and to keep the models updated during the system lifetime. Recently, data-driven solutions have received an immense attention in the industries systems for several practical reasons. First, these methods do not require the initial investment and expertise for developing accurate models. Moreover, it is possible to automatically update and retrain the diagnosers as the system or the environment change over time. Finally, unlike the model-based methods it is straight forward to combine time series measurements such as pressure and voltage with other sources of information such as system operating hours to achieve a higher accuracy. In this paper, we extend the traditional model-based fault detection and isolation concepts such as residuals, and detectable and isolable faults to the data-driven domain. We then propose an algorithm to automatically generate residuals from the normal operating data. We present the performance of our proposed approach through a comparative case study.

Differentiable architecture search (DARTS) is widely considered to be easy to overfit the validation set which leads to performance degradation. We first employ a series of exploratory experiments to verify that neither high-strength architecture parameters regularization nor warmup training scheme can effectively solve this problem. Based on the insights from the experiments, we conjecture that the performance of DARTS does not depend on the well-trained supernet weights and argue that the architecture parameters should be trained by the gradients which are obtained in the early stage rather than the final stage of training. This argument is then verified by exchanging the learning rate schemes of weights and parameters. Experimental results show that the simple swap of the learning rates can effectively solve the degradation and achieve competitive performance. Further empirical evidence suggests that the degradation is not a simple problem of the validation set overfitting but exhibit some links between the degradation and the operation selection bias within bilevel optimization dynamics. We demonstrate the generalization of this bias and propose to utilize this bias to achieve an operation-magnitude-based selective stop.