In recent work, the authors have developed a generic methodology for calibrating the noise in fluid dynamics stochastic partial differential equations where the stochasticity was introduced to parametrize subgrid-scale processes. The stochastic parameterization of sub-grid scale processes is required in the estimation of uncertainty in weather and climate predictions, to represent systematic model errors arising from subgrid-scale fluctuations. The previous methodology used a principal component analysis (PCA) technique based on the ansatz that the increments of the stochastic parametrization are normally distributed. In this paper, the PCA technique is replaced by a generative model technique. This enables us to avoid imposing additional constraints on the increments. The methodology is tested on a stochastic rotating shallow water model with the elevation variable of the model used as input data. The numerical simulations show that the noise is indeed non-Gaussian. The generative modelling technology gives good RMSE, CRPS score and forecast rank histogram results.

A growing trend involves integrating human knowledge into learning frameworks, leveraging subtle human feedback to refine AI models. Despite these advances, no comprehensive theoretical framework describing the specific conditions under which human comparisons improve the traditional supervised fine-tuning process has been developed. To bridge this gap, this paper studies the effective use of human comparisons to address limitations arising from noisy data and high-dimensional models. We propose a two-stage "Supervised Fine Tuning+Human Comparison" (SFT+HC) framework connecting machine learning with human feedback through a probabilistic bisection approach. The two-stage framework first learns low-dimensional representations from noisy-labeled data via an SFT procedure, and then uses human comparisons to improve the model alignment. To examine the efficacy of the alignment phase, we introduce a novel concept termed the "label-noise-to-comparison-accuracy" (LNCA) ratio. This paper theoretically identifies the conditions under which the "SFT+HC" framework outperforms pure SFT approach, leveraging this ratio to highlight the advantage of incorporating human evaluators in reducing sample complexity. We validate that the proposed conditions for the LNCA ratio are met in a case study conducted via an Amazon Mechanical Turk experiment.

With the spread and rapid advancement of black box machine learning models, the field of interpretable machine learning (IML) or explainable artificial intelligence (XAI) has become increasingly important over the last decade. This is particularly relevant for survival analysis, where the adoption of IML techniques promotes transparency, accountability and fairness in sensitive areas, such as clinical decision making processes, the development of targeted therapies, interventions or in other medical or healthcare related contexts. More specifically, explainability can uncover a survival model's potential biases and limitations and provide more mathematically sound ways to understand how and which features are influential for prediction or constitute risk factors. However, the lack of readily available IML methods may have deterred medical practitioners and policy makers in public health from leveraging the full potential of machine learning for predicting time-to-event data. We present a comprehensive review of the limited existing amount of work on IML methods for survival analysis within the context of the general IML taxonomy. In addition, we formally detail how commonly used IML methods, such as such as individual conditional expectation (ICE), partial dependence plots (PDP), accumulated local effects (ALE), different feature importance measures or Friedman's H-interaction statistics can be adapted to survival outcomes. An application of several IML methods to real data on data on under-5 year mortality of Ghanaian children from the Demographic and Health Surveys (DHS) Program serves as a tutorial or guide for researchers, on how to utilize the techniques in practice to facilitate understanding of model decisions or predictions.

Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the idea has led to many applications of importance weighting. For example, it is known that supervised learning under an assumption about the difference between the training and test distributions, called distribution shift, can guarantee statistically desirable properties through importance weighting by their density ratio. This survey summarizes the broad applications of importance weighting in machine learning and related research.

A weighted graph is used as an underlying structure of many algorithms like semisupervised learning and spectral clustering. If the edge weights are determined by a single similarity measure, then it hard if not impossible to capture all relevant aspects of similarity when using a single similarity measure. In particular, in the case of visual object matching it is beneficial to integrate different similarity measures that focus on different visual representations. In this paper, a novel approach to integrate multiple similarity measures is proposed. First pairs of similarity measures are combined with a diffusion process on their tensor product graph (TPG).

Statistical decision theory axiomatically assumes that the relative desirability of different options that humans perceive is well described by assigning them optionspecific scalar utility functions. However, this assumption is refuted by observed human behavior, including studies wherein preferences have been shown to change systematically simply through variation in the set of choice options presented. In this paper, we show that interpreting desirability as a relative comparison between available options at any particular decision instance results in a rational theory of value-inference that explains heretofore intractable violations of rational choice behavior in human subjects. Complementarily, we also characterize the conditions under which a rational agent selecting optimal options indicated by dynamic value inference in our framework will behave identically to one whose preferences are encoded using a static ordinal utility function.

This paper studies a novel discriminative part-based model to represent and recognize object shapes with an "And-Or graph". We define this model consisting of three layers: the leaf-nodes with collaborative edges for localizing local parts, the or-nodes specifying the switch of leaf-nodes, and the root-node encoding the global verification. A discriminative learning algorithm, extended from the CCCP [23], is proposed to train the model in a dynamical manner: the model structure (e.g., the configuration of the leaf-nodes associated with the or-nodes) is automatically determined with optimizing the multi-layer parameters during the iteration. The advantages of our method are two-fold.

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such a case, multiple criteria can be defined, and one can test for anomalies by scalarizing the multiple criteria using a linear combination of them. If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we introduce a novel non-parametric multi-criteria anomaly detection method using Pareto depth analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach scales linearly in the number of criteria and is provably better than linear combinations of the criteria.

We present a novel approach to tackle the ObjectNav task for non-stationary and potentially occluded targets in an indoor environment. We refer to this task Portable ObjectNav (or P-ObjectNav), and in this work, present its formulation, feasibility, and a navigation benchmark using a novel memory-enhanced LLM-based policy. In contrast to ObjNav where target object locations are fixed for each episode, P-ObjectNav tackles the challenging case where the target objects move during the episode. This adds a layer of time-sensitivity to navigation, and is particularly relevant in scenarios where the agent needs to find portable targets (e.g. misplaced wallets) in human-centric environments. The agent needs to estimate not just the correct location of the target, but also the time at which the target is at that location for visual grounding -- raising the question about the feasibility of the task. We address this concern by inferring results on two cases for object placement: one where the objects placed follow a routine or a path, and the other where they are placed at random. We dynamize Matterport3D for these experiments, and modify PPO and LLM-based navigation policies for evaluation. Using PPO, we observe that agent performance in the random case stagnates, while the agent in the routine-following environment continues to improve, allowing us to infer that P-ObjectNav is solvable in environments with routine-following object placement. Using memory-enhancement on an LLM-based policy, we set a benchmark for P-ObjectNav. Our memory-enhanced agent significantly outperforms their non-memory-based counterparts across object placement scenarios by 71.76% and 74.68% on average when measured by Success Rate (SR) and Success Rate weighted by Path Length (SRPL), showing the influence of memory on improving P-ObjectNav performance. Our code and dataset will be made publicly available.

Recently Large Language Models (LLMs) have showcased remarkable versatility across a spectrum of critical tasks. An LLM is adept at tasks such as copywriting, enhancing original sentences with their distinct style and voice, responding to knowledge base queries, generating code, solving mathematical problems, and performing classification or generation tasks tailored to user requirements. Moreover, there has been a recent expansion into multi-modal variants, such as Large Visual Language Models (LVLMs) or Large Multi-modal Language Models, which broaden their input/output capabilities to encompass various modalities. This evolution has significantly enhanced both the potential and range of applications of these models. In this survey, our primary focus is on Transformer-based Large Language Models (LLMs). The capability of LLMs is fundamentally rooted in their inference abilities, which dictates their proficiency in comprehending, processing, and providing solutions to various inquiries, as well as their adaptability to societally impactful domains.