Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to the arguments of nonlinear functions. Instead of only optimizing linear parameters, we optimize these additional nonlinear parameters with separable nonlinear least squared optimization using a variable projection algorithm. Both FFX and our new algorithm is applied on the PennML benchmark suite. We show that the proposed extensions of FFX leads to higher accuracy while providing models of similar length and with only a small increase in runtime on the given data. Our results are compared to a large set of regression methods that were already published for the given benchmark suite.

Industrial and scientific applications handle large volumes of data that render manual validation by humans infeasible. Therefore, we require automated data validation approaches that are able to consider the prior knowledge of domain experts to produce dependable, trustworthy assessments of data quality. Prior knowledge is often available as rules that describe interactions of inputs with regard to the target e.g. the target must be monotonically decreasing and convex over increasing input values. Domain experts are able to validate multiple such interactions at a glance. However, existing rule-based data validation approaches are unable to consider these constraints. In this work, we compare different shape-constrained regression algorithms for the purpose of data validation based on their classification accuracy and runtime performance.

We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the components are defined by loss functions (which include constraints), and the signal decomposition is carried out by minimizing the sum of losses of the components (subject to the constraints). When each loss function is the negative log-likelihood of a density for the signal component, this framework coincides with maximum a posteriori probability (MAP) estimation; but it also includes many other interesting cases. Summarizing and clarifying prior results, we give two distributed optimization methods for computing the decomposition, which find the optimal decomposition when the component class loss functions are convex, and are good heuristics when they are not. Both methods require only the masked proximal operator of each of the component loss functions, a generalization of the well-known proximal operator that handles missing entries in its argument. Both methods are distributed, i.e., handle each component separately. We derive tractable methods for evaluating the masked proximal operators of some loss functions that, to our knowledge, have not appeared in the literature.

This paper examines two different yet related questions related to explainable AI (XAI) practices. Machine learning (ML) is increasingly important in financial services, such as pre-approval, credit underwriting, investments, and various front-end and back-end activities. Machine Learning can automatically detect non-linearities and interactions in training data, facilitating faster and more accurate credit decisions. However, machine learning models are opaque and hard to explain, which are critical elements needed for establishing a reliable technology. The study compares various machine learning models, including single classifiers (logistic regression, decision trees, LDA, QDA), heterogeneous ensembles (AdaBoost, Random Forest), and sequential neural networks. The results indicate that ensemble classifiers and neural networks outperform. In addition, two advanced post-hoc model agnostic explainability techniques - LIME and SHAP are utilized to assess ML-based credit scoring models using the open-access datasets offered by US-based P2P Lending Platform, Lending Club. For this study, we are also using machine learning algorithms to develop new investment models and explore portfolio strategies that can maximize profitability while minimizing risk.

Function plays an important role in mathematics and many science branches. As the fast development of computer technology, more and more study on computational function analysis, e.g., Fast Fourier Transform, Wavelet Transform, Curve Function, are presented in these years. However, there are two main problems in these approaches: 1) hard to handle the complex functions of stationary and non-stationary, periodic and non-periodic, high order and low order; 2) hard to generalize the fitting functions from training data to test data. In this paper, a multiple regression based function fitting network that solves the two main problems is introduced as a predicable function fitting technique. This technique constructs the network includes three main parts: 1) the stationary transform layer, 2) the feature encoding layers, and 3) the fine tuning regression layer. The stationary transform layer recognizes the order of input function data, and transforms non-stationary function to stationary function. The feature encoding layers encode the raw input sequential data to a novel linear regression feature that can capture both the structural and the temporal characters of the sequential data. The fine tuning regression layer then fits the features to the target ahead values. The fitting network with the linear regression feature layers and a non-linear regression layer come up with high quality fitting results and generalizable predictions. The experiments of both mathematic function examples and the real word function examples verifies the efficiency of the proposed technique.

Federated learning, where algorithms are trained across multiple decentralized devices without sharing local data, is increasingly popular in distributed machine learning practice. Typically, a graph structure $G$ exists behind local devices for communication. In this work, we consider parameter estimation in federated learning with data distribution and communication heterogeneity, as well as limited computational capacity of local devices. We encode the distribution heterogeneity by parametrizing distributions on local devices with a set of distinct $p$-dimensional vectors. We then propose to jointly estimate parameters of all devices under the $M$-estimation framework with the fused Lasso regularization, encouraging an equal estimate of parameters on connected devices in $G$. We provide a general result for our estimator depending on $G$, which can be further calibrated to obtain convergence rates for various specific problem setups. Surprisingly, our estimator attains the optimal rate under certain graph fidelity condition on $G$, as if we could aggregate all samples sharing the same distribution. If the graph fidelity condition is not met, we propose an edge selection procedure via multiple testing to ensure the optimality. To ease the burden of local computation, a decentralized stochastic version of ADMM is provided, with convergence rate $O(T^{-1}\log T)$ where $T$ denotes the number of iterations. We highlight that, our algorithm transmits only parameters along edges of $G$ at each iteration, without requiring a central machine, which preserves privacy. We further extend it to the case where devices are randomly inaccessible during the training process, with a similar algorithmic convergence guarantee. The computational and statistical efficiency of our method is evidenced by simulation experiments and the 2020 US presidential election data set.

One of the simplest Machine learning algorithms out there, Linear Regression is used to make predictions on continuous dependent variables with knowledge from independent variables. A dependent variable is the effect, in which its value depends on changes in the independent variable. You may remember the line of best fit from school – this is what Linear Regression produces. A simple example is predicting one's weight depending on their height. Logistic Regression, similar to Linear Regression, is used to make predictions on categorical dependent variables with knowledge of independent variables.

We present a data-driven algorithm that advertisers can use to automate their digital ad-campaigns at online publishers. The algorithm enables the advertiser to search across available target audiences and ad-media to find the best possible combination for its campaign via online experimentation. The problem of finding the best audience-ad combination is complicated by a number of distinctive challenges, including (a) a need for active exploration to resolve prior uncertainty and to speed the search for profitable combinations, (b) many combinations to choose from, giving rise to high-dimensional search formulations, and (c) very low success probabilities, typically just a fraction of one percent. Our algorithm (designated LRDL, an acronym for Logistic Regression with Debiased Lasso) addresses these challenges by combining four elements: a multiarmed bandit framework for active exploration; a Lasso penalty function to handle high dimensionality; an inbuilt debiasing kernel that handles the regularization bias induced by the Lasso; and a semi-parametric regression model for outcomes that promotes cross-learning across arms. The algorithm is implemented as a Thompson Sampler, and to the best of our knowledge, it is the first that can practically address all of the challenges above. Simulations with real and synthetic data show the method is effective and document its superior performance against several benchmarks from the recent high-dimensional bandit literature.

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users' needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.

Software programs can increase their propensity to anticipate outcomes without being explicitly designed, thanks to artificial intelligence (AI) and machine learning (ML). Machine learning algorithms use previous data as input to anticipate new output values. Machine learning courses online are a modern invention that has benefited many workplace and company processes and students' daily lives. In this area of artificial intelligence (AI), statistical techniques are used to build smart computer systems that can pick up new information from readily available databases. The fields of computer science known as artificial intelligence (AI) and machine learning (ML) concentrate on analyzing and interpreting patterns and structures in data to allow understanding, reasoning, and decision-making independent of human involvement.