Fair Principal Component Analysis (PCA) is a problem setting where we aim to perform PCA while making the resulting representation fair in that the projected distributions, conditional on the sensitive attributes, match one another. However, existing approaches to fair PCA have two main problems: theoretically, there has been no statistical foundation of fair PCA in terms of learnability; practically, limited memory prevents us from using existing approaches, as they explicitly rely on full access to the entire data. On the theoretical side, we rigorously formulate fair PCA using a new notion called \emph{probably approximately fair and optimal} (PAFO) learnability. On the practical side, motivated by recent advances in streaming algorithms for addressing memory limitation, we propose a new setting called \emph{fair streaming PCA} along with a memory-efficient algorithm, fair noisy power method (FNPM). We then provide its {\it statistical} guarantee in terms of PAFO-learnability, which is the first of its kind in fair PCA literature. Lastly, we verify the efficacy and memory efficiency of our algorithm on real-world datasets.

Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive, unifying perspective on inverse decision modeling: a framework for learning parameterized representations of sequential decision behavior. First, we formalize the forward problem (as a normative standard), subsuming common classes of control behavior. Second, we use this to formalize the inverse problem (as a descriptive model), generalizing existing work on imitation/reward learning -- while opening up a much broader class of research problems in behavior representation. Finally, we instantiate this approach with an example (inverse bounded rational control), illustrating how this structure enables learning (interpretable) representations of (bounded) rationality -- while naturally capturing intuitive notions of suboptimal actions, biased beliefs, and imperfect knowledge of environments.

Computing properties of molecular systems rely on estimating expectations of the (unnormalized) Boltzmann distribution. Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities. However, stable simulations rely on very small integration time-steps ($10^{-15}\,\mathrm{s}$), whereas convergence of some moments, e.g. binding free energy or rates, might rely on sampling processes on time-scales as long as $10^{-1}\, \mathrm{s}$, and these simulations must be repeated for every molecular system independently. Here, we present Implict Transfer Operator (ITO) Learning, a framework to learn surrogates of the simulation process with multiple time-resolutions. We implement ITO with denoising diffusion probabilistic models with a new SE(3) equivariant architecture and show the resulting models can generate self-consistent stochastic dynamics across multiple time-scales, even when the system is only partially observed. Finally, we present a coarse-grained CG-SE3-ITO model which can quantitatively model all-atom molecular dynamics using only coarse molecular representations. As such, ITO provides an important step towards multiple time- and space-resolution acceleration of MD. Code is available at \href{https://github.com/olsson-group/ito}{https://github.com/olsson-group/ito}.

Although equivariant machine learning has proven effective at many tasks, success depends heavily on the assumption that the ground truth function is symmetric over the entire domain matching the symmetry in an equivariant neural network. A missing piece in the equivariant learning literature is the analysis of equivariant networks when symmetry exists only partially in the domain. In this work, we present a general theory for such a situation. We propose pointwise definitions of correct, incorrect, and extrinsic equivariance, which allow us to quantify continuously the degree of each type of equivariance a function displays. We then study the impact of various degrees of incorrect or extrinsic symmetry on model error. We prove error lower bounds for invariant or equivariant networks in classification or regression settings with partially incorrect symmetry. We also analyze the potentially harmful effects of extrinsic equivariance.

The fast adoption of new technologies forces companies to continuously adapt their operations making it harder to predict workforce requirements. Several recent studies have attempted to predict the emergence of new roles and skills in the labour market from online job ads. This paper aims to present a novel ontology linking business transformation initiatives to occupations and an approach to automatically populating it by leveraging embeddings extracted from job ads and Wikipedia pages on business transformation and emerging technologies topics. To our knowledge, no previous research explicitly links business transformation initiatives, like the adoption of new technologies or the entry into new markets, to the roles needed. Our approach successfully matches occupations to transformation initiatives under ten different scenarios, five linked to technology adoption and five related to business. This framework presents an innovative approach to guide enterprises and educational institutions on the workforce requirements for specific business transformation initiatives.

Algorithmic decision-making in high-stakes domains often involves assigning decisions to agents with incentives to strategically modify their input to the algorithm. In addition to dealing with incentives, in many domains of interest (e.g. lending and hiring) the decision-maker only observes feedback regarding their policy for rounds in which they assign a positive decision to the agent; this type of feedback is often referred to as apple tasting (or one-sided) feedback. We formalize this setting as an online learning problem with apple-tasting feedback where a principal makes decisions about a sequence of $T$ agents, each of which is represented by a context that may be strategically modified. Our goal is to achieve sublinear strategic regret, which compares the performance of the principal to that of the best fixed policy in hindsight, if the agents were truthful when revealing their contexts. Our main result is a learning algorithm which incurs $O (\sqrt{T})$ strategic regret when the sequence of agents is chosen stochastically. We also give an algorithm capable of handling adversarially-chosen agents, albeit at the cost of $O(T^{(d+1)/(d+2)})$ strategic regret (where $d$ is the dimension of the context). Our algorithms can be easily adapted to the setting where the principal receives bandit feedback -- this setting generalizes both the linear contextual bandit problem (by considering agents with incentives) and the strategic classification problem (by allowing for partial feedback).

There are several theories in economics regarding the roots or causes of prosperity in a society. One of these theories or hypotheses -- named geography hypothesis -- mentions that the reason why some countries are prosperous and some others are poor is the geographical location of the countries in the world as makes their climate and environment favorable or unfavorable regarding natural resources. Another competing hypothesis states that man-made institutions particularly inclusive political institutions are the reasons why some countries are prosperous and some others are poor. On the other hand, there is a specific political theory developed for the long-term social development in Iran -- named Arbitrary Rule and Aridisolatic Society which particularly emphasizes on the role of aridity to shape arbitrary political and economical institutions in Iran, without any functional social classes in the society. In this paper, by extending the AI-Economist -- a recently developed two-level multi-agent reinforcement learning environment -- I show that when the central planner is ruling the environment by arbitrary rules, the society evolves through different paths in different environments. In the environment having band-like vertical isolated patches of natural resources, all mobile agents are equally exploited by the central planner and the central planner is also not gaining any income, while in the society having more uniformly distributed natural resources, the productivity and Maximin are higher and the society generates a heterogeneous stratified social structure. All these findings provide a partial answer to the above debate and reconcile the role of geography and political institutions on the long-term development in a region.

Empirical risk minimization (ERM) is sensitive to spurious correlations in the training data, which poses a significant risk when deploying systems trained under this paradigm in high-stake applications. While the existing literature focuses on maximizing group-balanced or worst-group accuracy, estimating these accuracies is hindered by costly bias annotations. This study contends that current bias-unsupervised approaches to group robustness continue to rely on group information to achieve optimal performance. Firstly, these methods implicitly assume that all group combinations are represented during training. To illustrate this, we introduce a systematic generalization task on the MPI3D dataset and discover that current algorithms fail to improve the ERM baseline when combinations of observed attribute values are missing. Secondly, bias labels are still crucial for effective model selection, restricting the practicality of these methods in real-world scenarios. To address these limitations, we propose a revised methodology for training and validating debiased models in an entirely bias-unsupervised manner. We achieve this by employing pretrained self-supervised models to reliably extract bias information, which enables the integration of a logit adjustment training loss with our validation criterion. Our empirical analysis on synthetic and real-world tasks provides evidence that our approach overcomes the identified challenges and consistently enhances robust accuracy, attaining performance which is competitive with or outperforms that of state-of-the-art methods, which, conversely, rely on bias labels for validation.

With recent advances in large language models (LLMs), the concept of automatically generating children's educational materials has become increasingly realistic. Working toward the goal of age-appropriate simplicity in generated educational texts, we first examine the ability of several popular LLMs to generate stories with properly adjusted lexical and readability levels. We find that, in spite of the growing capabilities of LLMs, they do not yet possess the ability to limit their vocabulary to levels appropriate for younger age groups. As a second experiment, we explore the ability of state-of-the-art lexical simplification models to generalize to the domain of children's stories and, thus, create an efficient pipeline for their automatic generation. In order to test these models, we develop a dataset of child-directed lexical simplification instances, with examples taken from the LLM-generated stories in our first experiment. We find that, while the strongest-performing current lexical simplification models do not perform as well on material designed for children due to their reliance on large language models behind the scenes, some models that still achieve fairly strong results on general data can mimic or even improve their performance on children-directed data with proper fine-tuning, which we conduct using our newly created child-directed simplification dataset.

One of the challenges in language teaching is how best to organize rules regarding syntax, semantics, or phonology in a meaningful manner. This not only requires content creators to have pedagogical skills, but also have that language's deep understanding. While comprehensive materials to develop such curricula are available in English and some broadly spoken languages, for many other languages, teachers need to manually create them in response to their students' needs. This is challenging because i) it requires that such experts be accessible and have the necessary resources, and ii) describing all the intricacies of a language is time-consuming and prone to omission. In this work, we aim to facilitate this process by automatically discovering and visualizing grammar descriptions. We extract descriptions from a natural text corpus that answer questions about morphosyntax (learning of word order, agreement, case marking, or word formation) and semantics (learning of vocabulary). We apply this method for teaching two Indian languages, Kannada and Marathi, which, unlike English, do not have well-developed resources for second language learning. To assess the perceived utility of the extracted material, we enlist the help of language educators from schools in North America to perform a manual evaluation, who find the materials have potential to be used for their lesson preparation and learner evaluation.