Related papers: Structural Drift: The Population Dynamics of Seque…
One aim shared by multiple settings, such as continual learning or transfer learning, is to leverage previously acquired knowledge to converge faster on the current task. Usually this is done through fine-tuning, where an implicit…
We propose a new continuum model for random genetic drift by employing a dynamic boundary condition approach. The model can be viewed as a regularized version of the Kimura equation and admits a continuous solution. We establish the…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
We develop and analyze a general technique for learning with an unknown distribution drift. Given a sequence of independent observations from the last $T$ steps of a drifting distribution, our algorithm agnostically learns a family of…
The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time; as a consequence machine learning models may become inaccurate and need adjustment. While there do exist…
We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
In today's connected world, the generation of massive streaming data across diverse domains has become commonplace. In the presence of concept drift, class imbalance, label scarcity, and new class emergence, they jointly degrade…
Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutant spreads through the whole population…
We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc.\ Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed population of two…
Class-incremental learning of deep networks sequentially increases the number of classes to be classified. During training, the network has only access to data of one task at a time, where each task contains several classes. In this…
We consider the problem of causal discovery (structure learning) from heterogeneous observational data. Most existing methods assume a homogeneous sampling scheme, which leads to misleading conclusions when violated in many applications. To…
It is well-known that population structure is a catalyst for the evolution of cooperation since individuals can reciprocate with their neighbors through local interactions defined by network structures. Previous research typically relies on…
In the realm of time series analysis, tackling the phenomenon of concept drift poses a significant challenge. Concept drift -- characterized by the evolving statistical properties of time series data, affects the reliability and accuracy of…
Biological and artificial learners are inherently exposed to a stream of data and experience throughout their lifetimes and must constantly adapt to, learn from, or selectively ignore the ongoing input. Recent findings reveal that, even…
When deep learning models are sequentially trained on new data, they tend to abruptly lose performance on previously learned tasks, a critical failure known as catastrophic forgetting. This challenge severely limits the deployment of AI in…
The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. We are interested in an identification of those features, that are most relevant for the observed drift.…