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 Statistical Learning


Kernel PCA with the Nystr\"om method

arXiv.org Machine Learning

Kernel methods generalize classical statistical methods to discover non-linear patterns in data [Shawe-Taylor and Cristianini, 2004]. They have been demonstrated to achieve state-of-the-art results in many application domains and it is straightforward to apply them to non-numeric data, such as graphs or text [Vishwanathan et al., 2010, Lodhi et al., 2002]. Through a near arbitrary non-linear mapping of data points into a Hilbert space they offer remarkable flexibility whilst providing a precise mathematical framework for statistical analyses. A host of linear statistical methods have been adapted to be used with kernels, including Fisher discriminant analysis (FDA) [Mika et al., 1999], independent component analysis (ICA) [Bach and Jordan, 2002], instrumental variable (IV) regression [Singh et al., 2019], and many more. Kernel PCA is a non-linear version of principal component analysis (PCA), a ubiquitous method to discover the most important directions of variation in data [Pearson, 1901]. PCA may be used for dimensionality reduction, exploratory data analysis, anomaly detection, discriminant analysis, clustering, or as a general preprocessing step for regression or classification [Jolliffe, 2002, Wold et al., 1987]. The other side of the coin of kernel methods is their large computational requirements, as they generally scale in the number of data points rather than the number of data dimensions. As a remedy, various approximations have been proposed, such as the Nyström method, which randomly selects a smaller subset of data points and looks for solutions in their linear span. The Nyström method also plays an important role in recent state-of-the-art implementations of kernel methods [Rudi et al., 2017, Ma and Belkin, 2017, Meanti et al., 2020].


Estimating a new panel MSK dataset for comparative analyses of national absorptive capacity systems, economic growth, and development in low and middle income economies

arXiv.org Machine Learning

Within the national innovation system literature, empirical analyses are severely lacking for developing economies. Particularly, the low- and middle-income countries (LMICs) eligible for the World Bank's International Development Association (IDA) support, are rarely part of any empirical discourse on growth, development, and innovation. One major issue hindering panel analyses in LMICs, and thus them being subject to any empirical discussion, is the lack of complete data availability. This work offers a new complete panel dataset with no missing values for LMICs eligible for IDA's support. I use a standard, widely respected multiple imputation technique (specifically, Predictive Mean Matching) developed by Rubin (1987). This technique respects the structure of multivariate continuous panel data at the country level. I employ this technique to create a large dataset consisting of many variables drawn from publicly available established sources. These variables, in turn, capture six crucial country-level capacities: technological capacity, financial capacity, human capital capacity, infrastructural capacity, public policy capacity, and social capacity. Such capacities are part and parcel of the National Absorptive Capacity Systems (NACS). The dataset (MSK dataset) thus produced contains data on 47 variables for 82 LMICs between 2005 and 2019. The dataset has passed a quality and reliability check and can thus be used for comparative analyses of national absorptive capacities and development, transition, and convergence analyses among LMICs.


Feature Importance in Gradient Boosting Trees with Cross-Validation Feature Selection

arXiv.org Machine Learning

Gradient Boosting Machines (GBM) are among the go-to algorithms on tabular data, which produce state of the art results in many prediction tasks. Despite its popularity, the GBM framework suffers from a fundamental flaw in its base learners. Specifically, most implementations utilize decision trees that are typically biased towards categorical variables with large cardinalities. The effect of this bias was extensively studied over the years, mostly in terms of predictive performance. In this work, we extend the scope and study the effect of biased base learners on GBM feature importance (FI) measures. We show that although these implementation demonstrate highly competitive predictive performance, they still, surprisingly, suffer from bias in FI. By utilizing cross-validated (CV) unbiased base learners, we fix this flaw at a relatively low computational cost. We demonstrate the suggested framework in a variety of synthetic and real-world setups, showing a significant improvement in all GBM FI measures while maintaining relatively the same level of prediction accuracy.


The Importance of Location in Real Estate, Weather, and Machine Learning

#artificialintelligence

Real estate experts like to say that the three most important features of a property are: location, location, location! Likewise, weather events are highly location-dependent. We will see below how a similar perspective is also applicable to machine learning algorithms. In real estate, the buyer is first and foremost concerned about location for at least 3 reasons: (a) the desirability of the surrounding neighborhood; (b) the proximity to schools, businesses, services, etc.; and (c) the value of properties in that area. Similarly, meteorologists tell us that all weather is local.


Cognitive Analytics Answers the Question: What's Interesting in Your Data?

#artificialintelligence

Dimensionality reduction is a critical component of any solution dealing with massive data collections. Being able to sift through a mountain of data efficiently in order to find the key descriptive, predictive and explanatory features of the collection is a fundamental required capability for coping with the avalanche of data that all organizations are collecting. Identifying the most interesting dimensions of data is especially critical when integrating high-dimensional (high-variety) complex data sources, then attempting to visualize the most insightful patterns in the data, and then telling the data's story to your stakeholders. There is a "good news, bad news" angle here. First, the bad news: the human capacity for visualizing multiple dimensions is very limited: 3 or 4 dimensions are manageable; 5 or 6 dimensions are possible (e.g., with colors and symbols); but more dimensions are difficult-to-impossible to assimilate.


Intro to Deep Learning project in TensorFlow 2.x and Python - CouponED

#artificialintelligence

Welcome to the Course Introduction to Deep Learning with TensorFlow 2.0: In this course, you will learn advanced linear regression technique process and with this, you can be able to build any regression problem. Using this you can solve real-world problems like customer lifetime value, predictive analytics, etc. All the above-mentioned techniques are explained in TensorFlow. Problem Statement: A large child education toy company that sells educational tablets and gaming systems both online and in retail stores wanted to analyze the customer data. The goal of the problem is to determine the following objective as shown below.


Can We Forecast the Number of Sunspots?

#artificialintelligence

Firstly: what is a sunspot? Sunspots are a temporary phenomena on the Sun's photosphere that appear darker than the surrounding areas. The reason why I have selected the sunspots dataset for time series analysis is sunspots appear on an 11-year solar cycle, meaning we should expect to see a seasonality component to the data. I will be modelling the seasonality trend using two different methods, the ARMA model and LSTM model. The data that will be used is from 1749 to 2013 and is the monthly average at each month.


Top 10 Things You Should Never Say In A Data Science Interview

#artificialintelligence

Data science interviews can be cumbersome, and rejections are merely the beginning. While an academic degree, relevant training, skills, and course work are essential to break into data science, it does not guarantee a job or job satisfaction. When it comes to interviews, there are hundreds of reasons for a company to reject a candidate. Of course, it makes more sense for a company to reject a good candidate than to hire a bad one. But, a talented data science professional stands above all, making sure to stay ahead of the curve.


Important Clustering Algorithms in Machine Learning

#artificialintelligence

Clustering is a Machine Learning method. It is an unsupervised machine learning task. In which, we draw references from datasets consisting of input data without labelled responses. With a clustering algorithm, we give the algorithm a lot of input data with no labels and let it find any groupings in the data it can. We can use a clustering algorithm to categorize each data point into a specific group.


Complete Step-by-Step Gradient Descent Algorithm from Scratch

#artificialintelligence

If you've been studying machine learning long enough, you've probably heard terms such as SGD or Adam. They are two of many optimization algorithms. Optimization algorithms are the heart of machine learning which are responsible for the intricate work of machine learning models to learn from data. It turns out that optimization has been around for a long time, even outside of the machine learning realm. Investors seek to create portfolios that avoid excessive risk while achieving a high rate of return.