Related papers: Physics-Aware Learnability: From Set-Theoretic Ind…
We demonstrate that embedding physics-driven constraints into machine learning process can dramatically improve accuracy and generalizability of the resulting model. Physics-informed learning is illustrated on the example of analysis of…
We study the task of bandit learning, also known as best-arm identification, under the assumption that the true reward function f belongs to a known, but arbitrary, function class F. We seek a general theory of bandit learnability, akin to…
Mixed-effects models fit to observational practice data are widely used in learning analytics to estimate student-level variation in initial knowledge and learning rate, and the resulting estimates increasingly inform substantive claims…
Learning of advanced physics, requires a combination of empirical, conceptual and theoretical understanding. Students use a combination of these approaches to learn new material. Each student has different prior knowledge and will master…
It is well known that complete prior ignorance is not compatible with learning, at least in a coherent theory of (epistemic) uncertainty. What is less widely known, is that there is a state similar to full ignorance, that Walley calls…
We study robustness to test-time adversarial attacks in the regression setting with $\ell_p$ losses and arbitrary perturbation sets. We address the question of which function classes are PAC learnable in this setting. We show that classes…
Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those…
We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order…
The increasing adoption of machine learning tools has led to calls for accountability via model interpretability. But what does it mean for a machine learning model to be interpretable by humans, and how can this be assessed? We focus on…
In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain $\Omega$. The uniform Glivenko--Cantelli property…
While non-contextual hidden-variable theories are proved to be impossible, contextual ones are possible. In a contextual hidden-variable theory, an observable is called a beable if the hidden-variable assigns its value in a given…
Deploying machine learning models in safety-related do-mains (e.g. autonomous driving, medical diagnosis) demands for approaches that are explainable, robust against adversarial attacks and aware of the model uncertainty. Recent deep…
When some parameters of a constrained optimization problem (COP) are uncertain, this gives rise to a predict-then-optimize (PtO) problem, comprising two stages: the prediction of the unknown parameters from contextual information and the…
We present differentiable particle filters (DPFs): a differentiable implementation of the particle filter algorithm with learnable motion and measurement models. Since DPFs are end-to-end differentiable, we can efficiently train their…
Learning governing dynamics from data is a common goal across the sciences, yet it is only well-posed when the underlying mechanisms are identifiable. In practice, many data-driven methods implicitly assume identifiability; when this…
Imitation learning often assumes that demonstrations are close to optimal according to some fixed, but unknown, cost function. However, according to satisficing theory, humans often choose acceptable behavior based on their personal (and…
In this work, we consider the problem of identifying an unknown linear dynamical system given a finite hypothesis class. In particular, we analyze the effect of the excitation input on the sample complexity of identifying the true system…
The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…
In practical applications, we can rarely assume full observability of a system's environment, despite such knowledge being important for determining a reactive control system's precise interaction with its environment. Therefore, we propose…
Although a recent shift has been made in the field of predictive process monitoring to use models from the explainable artificial intelligence field, the evaluation still occurs mainly through performance-based metrics, thus not accounting…