Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze non-stationary processes, and yet most time-series analysis methods that are used in practice, on important problems across science and industry, make the simplifying assumption of stationarity. One important problem in the analysis of non-stationary systems is the problem class that we refer to as Parameter Inference from a Non-stationary Unknown Process (PINUP). Given an observed time series, this involves inferring the parameters that drive non-stationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here we review and unify a diverse literature of algorithms for PINUP. We formulate the problem, and categorize the various algorithmic contributions. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on - notably the non-stationary Lorenz process and logistic map - are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing non-stationary systems and suggest new directions for progress on the PINUP problem and the broader study of non-stationary phenomena.

Although Multimodal Large Language Models (MLLMs) have demonstrated promising versatile capabilities, their performance is still inferior to specialized models on downstream tasks, which makes adaptation necessary to enhance their utility. However, fine-tuning methods require independent training for every model, leading to huge computation and memory overheads. In this paper, we propose a novel setting where we aim to improve the performance of diverse MLLMs with a group of shared parameters optimized for a downstream task. To achieve this, we propose Transferable Visual Prompting (TVP), a simple and effective approach to generate visual prompts that can transfer to different models and improve their performance on downstream tasks after trained on only one model. We introduce two strategies to address the issue of cross-model feature corruption of existing visual prompting methods and enhance the transferability of the learned prompts, including 1) Feature Consistency Alignment: which imposes constraints to the prompted feature changes to maintain task-agnostic knowledge; 2) Task Semantics Enrichment: which encourages the prompted images to contain richer task-specific semantics with language guidance. We validate the effectiveness of TVP through extensive experiments with 6 modern MLLMs on a wide variety of tasks ranging from object recognition and counting to multimodal reasoning and hallucination correction.

Time-varying parameters (TVPs) models are frequently used in economics to model structural change. I show that they are in fact ridge regressions. Instantly, this makes computations, tuning, and implementation much easier than in the state-space paradigm. Among other things, solving the equivalent dual ridge problem is computationally very fast even in high dimensions, and the crucial "amount of time variation" is tuned by cross-validation. Evolving volatility is dealt with using a two-step ridge regression. I consider extensions that incorporate sparsity (the algorithm selects which parameters vary and which do not) and reduced-rank restrictions (variation is tied to a factor model). To demonstrate the usefulness of the approach, I use it to study the evolution of monetary policy in Canada. The application requires the estimation of about 4600 TVPs, a task well within the reach of the new method.