This course will introduce you to some of the most widely used predictive modeling techniques and their core principles. Models such as multiple linear regression, logistic regression, auto-regressive integrated moving average (ARIMA), decision trees, and neural networks are frequently used in solving predictive analytics problems.

Background and objective: Stacking is an ensemble machine learning method that averages predictions from multiple other algorithms, such as generalized linear models and regression trees. A recent iteration of stacking, called super learning, has been developed as a general approach to black box supervised learning and has seen frequent usage, in part due to the availability of an R package. I develop super learning in the SAS software system using a new macro, and demonstrate its performance relative to the R package. Methods: I follow closely previous work using the R SuperLearner package and assess the performance of super learning in a number of domains. I compare the R package with the new SAS macro in a small set of simulations assessing curve fitting in a prediction model, a set of 14 publicly available datasets to assess cross-validated, expected loss, and data from a randomized trial of job seekers' training to assess the utility of super learning in causal inference using inverse probability weighting. Results: Across the simulated data and the publicly available data, the macro performed similarly to the R package, even with a different set of potential algorithms available natively in R and SAS. The example with inverse probability weighting demonstrated the ability of the SAS macro to include algorithms developed in R. Conclusions: The super learner macro performs as well as the R package at a number of tasks. Further, by extending the macro to include the use of R packages, the macro can leverage both the robust, enterprise oriented procedures in SAS and the nimble, cutting edge packages in R. In the spirit of ensemble learning, this macro extends the potential library of algorithms beyond a single software system and provides a simple avenue into machine learning in SAS.

We present a novel inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a Hessian-vector product from first-order information. In theory, our method efficiently computes the statistical error covariance in $M$-estimation, both for unregularized convex learning problems and high-dimensional LASSO regression, without using exact second order information, or resampling the entire data set. In practice, we demonstrate the effectiveness of our framework on large-scale machine learning problems, that go even beyond convexity: as a highlight, our work can be used to detect certain adversarial attacks on neural networks.

CBL U Cambridge, UK Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability proofs for nonlinear ICA have been proposed, leveraging the temporal structure of the independent components. Here, we propose a general framework for nonlinear ICA, which, as a special case, can make use of temporal structure. It is based on augmenting the data by an auxiliary variable, such as the time index, the history of the time series, or any other available information. We propose to learn nonlinear ICA by discriminating between true augmented data, or data in which the auxiliary variable has been randomized. This enables the framework to be implemented algorithmically through logistic regression, possibly in a neural network. We provide a comprehensive proof of the identifiability of the model as well as the consistency of our estimation method. The approach not only provides a general theoretical framework combining and generalizing previously proposed nonlinear ICA models and algorithms, but also brings practical advantages.

Coresets are one of the central methods to facilitate the analysis of large data sets. We continue a recent line of research applying the theory of coresets to logistic regression. First, we show a negative result, namely, that no strongly sublinear sized coresets exist for logistic regression. To deal with intractable worst-case instances we introduce a complexity measure $\mu(X)$, which quantifies the hardness of compressing a data set for logistic regression. $\mu(X)$ has an intuitive statistical interpretation that may be of independent interest. For data sets with bounded $\mu(X)$-complexity, we show that a novel sensitivity sampling scheme produces the first provably sublinear $(1\pm\varepsilon)$-coreset. We illustrate the performance of our method by comparing to uniform sampling as well as to state of the art methods in the area. The experiments are conducted on real world benchmark data for logistic regression.

We consider the task of training classifiers without labels. We propose a weakly supervised method---adversarial label learning---that trains classifiers to perform well against an adversary that chooses labels for training data. The weak supervision constrains what labels the adversary can choose. The method therefore minimizes an upper bound of the classifier's error rate using projected primal-dual subgradient descent. Minimizing this bound protects against bias and dependencies in the weak supervision. Experiments on three real datasets show that our method can train without labels and outperforms other approaches for weakly supervised learning.

There are hundred of types of logistic regression, some for categorical variables, some with curious names such as Poisson regression. It is confusing for the expert, and even more for the beginner, and for your boss. If you transform your response (often a proportion or a binary response such as fraud or no fraud in this context) you can instead use a linear regression. While purists claim that an actual logistic regression is more precise (from a theoretical perspective), model precision is irrelevant: it is the quality of your data that matters. A model with 1% extra accuracy does not help if your data has 20% of noise, or your theoretical model is a rough approximation of the reality.

For me, studying Logistic regression first helped a lot when I started to learn Neural Networks. You can think of each neuron in the network as a Logistic Regression, it has the input, the weights, the bias you do a dot product to all of that, then apply some non linear function. Moreover, the final layer of a neural network is a simple linear model (most of the time). Let's look closer at the "output layer", you can see that this is a simple linear (or logistic) regression, we have the input (hidden layer 2), we have the weighs, we do a dot product and then add a non linear function (depends on the task). The first part (on the left) is trying to learn a good representation of the data that will help the second part (on the right) to perform a linear classification/regression.

This work includes a number of novel contributions for the multiple-source adaptation problem. We present new normalized solutions with strong theoretical guarantees for the cross-entropy loss and other similar losses. We also provide new guarantees that hold in the case where the conditional probabilities for the source domains are distinct. Moreover, we give new algorithms for determining the distribution-weighted combination solution for the cross-entropy loss and other losses. We report the results of a series of experiments with real-world datasets. We find that our algorithm outperforms competing approaches by producing a single robust model that performs well on any target mixture distribution. Altogether, our theory, algorithms, and empirical results provide a full solution for the multiple-source adaptation problem with very practical benefits.

Sparsification is becoming more and more relevant with the proliferation of huge data sets. Coresets are a principled way to construct representative weighted subsets of a data set that have matching performance with the full data set for specific problems. However, coreset language neglects the nature of the underlying data distribution, which is often continuous. In this paper, we address this oversight by introducing a notion of measure coresets that generalizes coreset language to arbitrary probability measures. Our definition reveals a surprising connection to optimal transport theory which we leverage to design a coreset for problems with Lipschitz costs. We validate our construction on support vector machine (SVM) training, k-means clustering, k-median clustering, and linear regression and show that we are competitive with previous coreset constructions.