Support Vector Machines (SVM) are one of the most powerful machine learning models around, and this topic has been one that students have requested ever since I started making courses. These days, everyone seems to be talking about deep learning, but in fact there was a time when support vector machines were seen as superior to neural networks. One of the things you'll learn about in this course is that a support vector machine actually is a neural network, and they essentially look identical if you were to draw a diagram. The toughest obstacle to overcome when you're learning about support vector machines is that they are very theoretical. This theory very easily scares a lot of people away, and it might feel like learning about support vector machines is beyond your ability.

Multiplying the weights with the adjacency matrix means that all the feature vectors of all (1-hop) neighboring nodes are summed and aggregated for every node. However, the feature vector of the node itself is not included. To address this, Kipf and Welling [4] add the identity matrix to the adjacency matrix and denote this new matrix  A I. Multiplication of the adjacency matrix will also change the scale of the feature vectors.

Machine Learning is like sex in high school. Everyone is talking about it, a few know what to do, and only your teacher is doing it. So here it is, a simple introduction for those who always wanted to understand machine learning. Whether you are a programmer or a manager. The first methods came from pure statistics in the 50's.

Subtyping of Alzheimer's disease (AD) can facilitate diagnosis, treatment, prognosis and disease management. It can also support the testing of new prevention and treatment strategies through clinical trials. In this study, we employed spectral clustering to cluster 29,922 AD patients in the OneFlorida Data Trust using their longitudinal EHR data of diagnosis and conditions into four subtypes. In addition, according to the results of various statistical tests, these subtypes are also significantly different with respect to demographics, mortality, and prescription medications after the AD diagnosis. This study could potentially facilitate early detection and personalized treatment of AD as well as data-driven generalizability assessment of clinical trials for AD. Introduction Alzheimer's disease (AD) is a progressive neurodegenerative disorder that affects an estimated 6.2 million Americans age 65 and older in 2021. This number is likely to reach 13.8 million by 2060.

Energy disaggregation, known in the literature as Non-Intrusive Load Monitoring (NILM), is the task of inferring the energy consumption of each appliance given the aggregate signal recorded by a single smart meter. In this paper, we propose a novel two-stage optimization-based approach for energy disaggregation. In the first phase, a small training set consisting of disaggregated power profiles is used to estimate the parameters and the power states by solving a mixed integer programming problem. Once the model parameters are estimated, the energy disaggregation problem is formulated as a constrained binary quadratic optimization problem. We incorporate penalty terms that exploit prior knowledge on how the disaggregated traces are generated, and appliance-specific constraints characterizing the signature of different types of appliances operating simultaneously. Our approach is compared with existing optimization-based algorithms both on a synthetic dataset and on three real-world datasets. The proposed formulation is computationally efficient, able to disambiguate loads with similar consumption patterns, and successfully reconstruct the signatures of known appliances despite the presence of unmetered devices, thus overcoming the main drawbacks of the optimization-based methods available in the literature.

The foremost challenge to causal inference with real-world data is to handle the imbalance in the covariates with respect to different treatment options, caused by treatment selection bias. To address this issue, recent literature has explored domain-invariant representation learning based on different domain divergence metrics (e.g., Wasserstein distance, maximum mean discrepancy, position-dependent metric, and domain overlap). In this paper, we reveal the weaknesses of these strategies, i.e., they lead to the loss of predictive information when enforcing the domain invariance; and the treatment effect estimation performance is unstable, which heavily relies on the characteristics of the domain distributions and the choice of domain divergence metrics. Motivated by information theory, we propose to learn the Infomax and Domain-Independent Representations to solve the above puzzles. Our method utilizes the mutual information between the global feature representations and individual feature representations, and the mutual information between feature representations and treatment assignment predictions, in order to maximally capture the common predictive information for both treatment and control groups. Moreover, our method filters out the influence of instrumental and irrelevant variables, and thus it effectively increases the predictive ability of potential outcomes. Experimental results on both the synthetic and real-world datasets show that our method achieves state-of-the-art performance on causal effect inference. Moreover, our method exhibits reliable prediction performances when facing data with different characteristics of data distributions, complicated variable types, and severe covariate imbalance.

Despite perfectly interpolating the training data, deep neural networks (DNNs) can often generalize fairly well, in part due to the "implicit regularization" induced by the learning algorithm. Nonetheless, various forms of regularization, such as "explicit regularization" (via weight decay), are often used to avoid overfitting, especially when the data is corrupted. There are several challenges with explicit regularization, most notably unclear convergence properties. Inspired by convergence properties of stochastic mirror descent (SMD) algorithms, we propose a new method for training DNNs with regularization, called regularizer mirror descent (RMD). In highly overparameterized DNNs, SMD simultaneously interpolates the training data and minimizes a certain potential function of the weights. RMD starts with a standard cost which is the sum of the training loss and a convex regularizer of the weights. Reinterpreting this cost as the potential of an "augmented" overparameterized network and applying SMD yields RMD. As a result, RMD inherits the properties of SMD and provably converges to a point "close" to the minimizer of this cost. RMD is computationally comparable to stochastic gradient descent (SGD) and weight decay, and is parallelizable in the same manner. Our experimental results on training sets with various levels of corruption suggest that the generalization performance of RMD is remarkably robust and significantly better than both SGD and weight decay, which implicitly and explicitly regularize the $\ell_2$ norm of the weights. RMD can also be used to regularize the weights to a desired weight vector, which is particularly relevant for continual learning.

In this work, we improve upon the guarantees for sparse random embeddings, as they were recently provided and analyzed by Freksen at al. (NIPS'18) and Jagadeesan (NIPS'19). Specifically, we show that (a) our bounds are explicit as opposed to the asymptotic guarantees provided previously, and (b) our bounds are guaranteed to be sharper by practically significant constants across a wide range of parameters, including the dimensionality, sparsity and dispersion of the data. Moreover, we empirically demonstrate that our bounds significantly outperform prior works on a wide range of real-world datasets, such as collections of images, text documents represented as bags-of-words, and text sequences vectorized by neural embeddings. Behind our numerical improvements are techniques of broader interest, which improve upon key steps of previous analyses in terms of (c) tighter estimates for certain types of quadratic chaos, (d) establishing extreme properties of sparse linear forms, and (e) improvements on bounds for the estimation of sums of independent random variables.

Estimating heterogeneous treatment effects in domains such as healthcare or social science often involves sensitive data where protecting privacy is important. We introduce a general meta-algorithm for estimating conditional average treatment effects (CATE) with differential privacy (DP) guarantees. Our meta-algorithm can work with simple, single-stage CATE estimators such as S-learner and more complex multi-stage estimators such as DR and R-learner. We perform a tight privacy analysis by taking advantage of sample splitting in our meta-algorithm and the parallel composition property of differential privacy. In this paper, we implement our approach using DP-EBMs as the base learner. DP-EBMs are interpretable, high-accuracy models with privacy guarantees, which allow us to directly observe the impact of DP noise on the learned causal model. Our experiments show that multi-stage CATE estimators incur larger accuracy loss than single-stage CATE or ATE estimators and that most of the accuracy loss from differential privacy is due to an increase in variance, not biased estimates of treatment effects.

We propose an extended generalization of the pseudo Huber loss formulation. We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex losses with robust loss functions. With this formulation, we show that a linear convergence algorithm can be utilized to find a minimizer. We further discuss the creation of a quasi-convex composite loss and provide a derivative-free exponential convergence rate algorithm.