Copyright policies play a pivotal role in protecting the intellectual property of creators and companies in creative industries. The advent of cost-reducing technologies, such as generative AI, in these industries calls for renewed attention to the role of these policies. This paper studies product positioning and competition in a market of creatively differentiated products and the competitive and welfare effects of copyright protection. A common feature of products with creative elements is that their key attributes (e.g., images and text) are unstructured and thus high-dimensional. We focus on a stylized design product, fonts, and use data from the world's largest online marketplace for fonts. We use neural network embeddings to quantify unstructured attributes and measure the visual similarity. We show that this measure closely aligns with actual human perception. Based on this measure, we empirically find that competitions occur locally in the visual characteristics space. We then develop a structural model for supply and demand that integrate the embeddings. Through counterfactual analyses, we find that local copyright protection can enhance consumer welfare when products are relocated, and the interplay between copyright and cost-reducing technologies is essential in determining an optimal policy for social welfare. We believe that the embedding analysis and empirical models introduced in this paper can be applicable to a range of industries where unstructured data captures essential features of products and markets.

Ridge regression is a method we can use to fit a regression model when multicollinearity is present in the data. This second term in the equation is known as a shrinkage penalty. In ridge regression, we select a value for λ that produces the lowest possible test MSE (mean squared error). This tutorial provides a step-by-step example of how to perform ridge regression in R. For this example, we'll use the R built-in dataset called mtcars. To perform ridge regression, we'll use functions from the glmnet package.

We extend best-subset selection to linear Multi-Task Learning (MTL), where a set of linear models are jointly trained on a collection of datasets (``tasks''). Allowing the regression coefficients of tasks to have different sparsity patterns (i.e., different supports), we propose a modeling framework for MTL that encourages models to share information across tasks, for a given covariate, through separately 1) shrinking the coefficient supports together, and/or 2) shrinking the coefficient values together. This allows models to borrow strength during variable selection even when the coefficient values differ markedly between tasks. We express our modeling framework as a Mixed-Integer Program, and propose efficient and scalable algorithms based on block coordinate descent and combinatorial local search. We show our estimator achieves statistically optimal prediction rates. Importantly, our theory characterizes how our estimator leverages the shared support information across tasks to achieve better variable selection performance. We evaluate the performance of our method in simulations and two biology applications. Our proposed approaches outperform other sparse MTL methods in variable selection and prediction accuracy. Interestingly, penalties that shrink the supports together often outperform penalties that shrink the coefficient values together. We will release an R package implementing our methods.

Artificial intelligence (AI) technologies have become increasingly widespread over the last decade. As the use of AI has become more common and the performance of AI systems has improved, policymakers, scholars, and advocates have raised concerns. Policy and ethical issues such as algorithmic bias, data privacy, and transparency have gained increasing attention, raising calls for policy and regulatory changes to address the potential consequences of AI (Acemoglu 2021). As AI continues to improve and diffuse, it will likely have significant long-term implications for jobs, inequality, organizations, and competition. Premature deployment of AI products can also aggravate existing biases and discrimination or violate data privacy and protection practices.

Cross-study replicability is a powerful model evaluation criterion that emphasizes generalizability of predictions. When training cross-study replicable prediction models, it is critical to decide between merging and treating the studies separately. We study boosting algorithms in the presence of potential heterogeneity in predictor-outcome relationships across studies and compare two multi-study learning strategies: 1) merging all the studies and training a single model, and 2) multi-study ensembling, which involves training a separate model on each study and ensembling the resulting predictions. In the regression setting, we provide theoretical guidelines based on an analytical transition point to determine whether it is more beneficial to merge or to ensemble for boosting with linear learners. In addition, we characterize a bias-variance decomposition of estimation error for boosting with component-wise linear learners. We verify the theoretical transition point result in simulation and illustrate how it can guide the decision on merging vs. ensembling in an application to breast cancer gene expression data.

This article was written by Prashant Gupta. One of the major aspects of training your machine learning model is avoiding overfitting. The model will have a low accuracy if it is overfitting. This happens because your model is trying too hard to capture the noise in your training dataset. By noise we mean the data points that don't really represent the true properties of your data, but random chance.

In this paper, we introduce the weighted-average quantile regression framework, $\int_0^1 q_{Y|X}(u)\psi(u)du = X'\beta$, where $Y$ is a dependent variable, $X$ is a vector of covariates, $q_{Y|X}$ is the quantile function of the conditional distribution of $Y$ given $X$, $\psi$ is a weighting function, and $\beta$ is a vector of parameters. We argue that this framework is of interest in many applied settings and develop an estimator of the vector of parameters $\beta$. We show that our estimator is $\sqrt T$-consistent and asymptotically normal with mean zero and easily estimable covariance matrix, where $T$ is the size of available sample. We demonstrate the usefulness of our estimator by applying it in two empirical settings. In the first setting, we focus on financial data and study the factor structures of the expected shortfalls of the industry portfolios. In the second setting, we focus on wage data and study inequality and social welfare dependence on commonly used individual characteristics.

In this paper, we study endogeneity problems in algorithmic decision-making where data and actions are interdependent. When there are endogenous covariates in a contextual multi-armed bandit model, a novel bias (self-fulfilling bias) arises because the endogeneity of the covariates spills over to the actions. We propose a class of algorithms to correct for the bias by incorporating instrumental variables into leading online learning algorithms. These algorithms also attain regret levels that match the best known lower bound for the cases without endogeneity. To establish the theoretical properties, we develop a general technique that untangles the interdependence between data and actions.

Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon Optimization (DySMHO), a scalable machine learning framework for identifying governing laws in the form of differential equations from large-scale noisy experimental data sets. DySMHO consists of a novel moving horizon dynamic optimization strategy that sequentially learns the underlying governing equations from a large dictionary of basis functions. The sequential nature of DySMHO allows leveraging statistical arguments for eliminating irrelevant basis functions, avoiding overfitting to recover accurate and parsimonious forms of the governing equations. Canonical nonlinear dynamical system examples are used to demonstrate that DySMHO can accurately recover the governing laws, is robust to high levels of measurement noise and that it can handle challenges such as multiple time scale dynamics.

In this article, we developed and analyzed a thresholding method in which soft thresholding estimators are independently expanded by empirical scaling values. The scaling values have a common hyper-parameter that is an order of expansion of an ideal scaling value that achieves hard thresholding. We simply call this estimator a scaled soft thresholding estimator. The scaled soft thresholding is a general method that includes the soft thresholding and non-negative garrote as special cases and gives an another derivation of adaptive LASSO. We then derived the degree of freedom of the scaled soft thresholding by means of the Stein's unbiased risk estimate and found that it is decomposed into the degree of freedom of soft thresholding and the reminder connecting to hard thresholding. In this meaning, the scaled soft thresholding gives a natural bridge between soft and hard thresholding methods. Since the degree of freedom represents the degree of over-fitting, this result implies that there are two sources of over-fitting in the scaled soft thresholding. The first source originated from soft thresholding is determined by the number of un-removed coefficients and is a natural measure of the degree of over-fitting. We analyzed the second source in a particular case of the scaled soft thresholding by referring a known result for hard thresholding. We then found that, in a sparse, large sample and non-parametric setting, the second source is largely determined by coefficient estimates whose true values are zeros and has an influence on over-fitting when threshold levels are around noise levels in those coefficient estimates. In a simple numerical example, these theoretical implications has well explained the behavior of the degree of freedom. Moreover, based on the results here and some known facts, we explained the behaviors of risks of soft, hard and scaled soft thresholding methods.