Observational cohort studies with oversampled exposed subjects are typically implemented to understand the causal effect of a rare exposure. Because the distribution of exposed subjects in the sample differs from the source population, estimation of a propensity score function (i.e., probability of exposure given baseline covariates) targets a nonparametrically nonidentifiable parameter. Consistent estimation of propensity score functions is an important component of various causal inference estimators, including double robust machine learning and inverse probability weighted estimators. We propose the use of the probability of exposure from the source population in observation-weighted stacking algorithms to produce consistent estimators of propensity score functions. Simulation studies and a hypothetical health policy intervention data analysis demonstrate low empirical bias and variance for these stacked propensity score functions with observation weights.

The purpose of this paper is to indicate that the recently proposed Momentum fractional least mean squares (mFLMS) algorithm has some serious flaws in its design and analysis. Our apprehensions are based on the evidence we found in the derivation and analysis in the paper titled: \textquotedblleft \textit{Momentum fractional LMS for power signal parameter estimation}\textquotedblright. In addition to the theoretical bases our claims are also verified through extensive simulation results. The experiments clearly show that the new method does not have any advantage over the classical least mean square (LMS) method.

Multi-output Gaussian processes (MOGP) generalise the powerful Gaussian process (GP) predictive model to the vector-valued random field setup (Alvarez et al., 2012). It has been experimentally shown that by simultaneously exploiting correlations between multiple outputs and across the input space, it is possible to provide better predictions, particularly in scenarios with missing or noisy data (Bonilla et al., 2008; Dai et al., 2017). The main focus in the literature for MOGP has been on the definition of a suitable cross-covariance function between the multiple outputs that allows for the treatment of outputs as a single GP with a properly defined covariance function (Alvarez et al., 2012). The two classical alternatives to define such cross-covariance functions are the linear model of coregionalisation (LMC) (Journel and Huijbregts, 1978) and process convolutions (Higdon, 2002). In the former case, each output corresponds to a weighted sum of shared latent random functions.

Boosted decision trees enjoy popularity in a variety of applications; however, for large-scale datasets, the cost of training a decision tree in each round can be prohibitively expensive. Inspired by ideas from the multi-arm bandit literature, we develop a highly efficient algorithm for computing exact greedy-optimal decision trees, outperforming the state-of-the-art Quick Boost method. We further develop a framework for deriving lower bounds on the problem that applies to a wide family of conceivable algorithms for the task (including our algorithm and Quick Boost), and we demonstrate empirically on a wide variety of data sets that our algorithm is near-optimal within this family of algorithms. We also derive a lower bound applicable to any algorithm solving the task, and we demonstrate that our algorithm empirically achieves performance close to this best-achievable lower bound.

Multitask learning has shown promising performance in many applications and many multitask models have been proposed. In order to identify an effective multitask model for a given multitask problem, we propose a learning framework called learning to multitask (L2MT). To achieve the goal, L2MT exploits historical multitask experience which is organized as a training set consists of several tuples, each of which contains a multitask problem with multiple tasks, a multitask model, and the relative test error. Based on such training set, L2MT first uses a proposed layerwise graph neural network to learn task embeddings for all the tasks in a multitask problem and then learns an estimation function to estimate the relative test error based on task embeddings and the representation of the multitask model based on a unified formulation. Given a new multitask problem, the estimation function is used to identify a suitable multitask model. Experiments on benchmark datasets show the effectiveness of the proposed L2MT framework.

Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture. This mechanism has been used with the Otter and Prover9 theorem provers, both for interactive formalizations and for human-assisted proving of open conjectures in small theories. In this work we explore the use of watchlists in large theories coming from first-order translations of large ITP libraries, aiming at improving hammer-style automation by smarter internal guidance of the ATP systems. In particular, we (i) design watchlist-based clause evaluation heuristics inside the E ATP system, and (ii) develop new proof guiding algorithms that load many previous proofs inside the ATP and focus the proof search using a dynamically updated notion of proof matching. The methods are evaluated on a large set of problems coming from the Mizar library, showing significant improvement of E's standard portfolio of strategies, and also of the previous best set of strategies invented for Mizar by evolutionary methods.

I created a custom'particle optimizer' and published a pip python package called kernelml. The motivation for making this algorithm was to give analysts and data scientists a generalized machine learning algorithm for complex loss functions and non-linear coefficients. The optimizer uses a combination of simple machine learning and probabilistic simulations to search for optimal parameters using a loss function, input and output matrices, and (optionally) a random sampler. I'm currently working on more features and hope to eventually make the project open source. Let's take the problem of clustering longitude and latitude coordinates.

Introduction Lesson 1: Building Foundational Python Skills for Data Analytics Lesson 1 covers the Python tools commonly used for data analysis. Lesson 2: Analyzing Data Using Simulations and Resampling In Lesson 2 we apply the Python data analysis tools to building simulations and computing statistics. The techniques for resampling statistics are both powerful and easy to learn. They express big ideas with very little code. Lesson 3: Improving Reliability with MyPy and Typing Hinting In the first half of Lesson 3, we wade deeper into Python's tools for organizing and analyzing data.

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model minimizes the worst case (maximum) of Stein's loss across all normal reference distributions within a prescribed Wasserstein distance from the normal distribution characterized by the sample mean and the sample covariance matrix. We prove that this estimation problem is equivalent to a semidefinite program that is tractable in theory but beyond the reach of general purpose solvers for practically relevant problem dimensions $p$. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear shrinkage estimator. Besides being invertible and well-conditioned even for $p>n$, the new shrinkage estimator is rotation-equivariant and preserves the order of the eigenvalues of the sample covariance matrix. These desirable properties are not imposed ad hoc but emerge naturally from the underlying distributionally robust optimization model. Finally, we develop a sequential quadratic approximation algorithm for efficiently solving the general estimation problem subject to conditional independence constraints typically encountered in Gaussian graphical models.

In this paper, we propose to provide a general ensemble learning framework based on deep learning models. Given a group of unit models, the proposed deep ensemble learning framework will effectively combine their learning results via a multilayered ensemble model. In the case when the unit model mathematical mappings are bounded, sigmoidal and discriminatory, we demonstrate that the deep ensemble learning framework can achieve a universal approximation of any functions from the input space to the output space. Meanwhile, to achieve such a performance, the deep ensemble learning framework also impose a strict constraint on the number of involved unit models. According to the theoretic proof provided in this paper, given the input feature space of dimension d, the required unit model number will be 2d, if the ensemble model involves one single layer. Furthermore, as the ensemble component goes deeper, the number of required unit model is proved to be lowered down exponentially.