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Bayesian optimal design of experiments is a well-established approach to planning experiments. Briefly, a probability distribution, known as a statistical model, for the responses is assumed which is dependent on a vector of unknown parameters. A utility function is then specified which gives the gain in information for estimating the true value of the parameters using the Bayesian posterior distribution. A Bayesian optimal design is given by maximising the expectation of the utility with respect to the joint distribution given by the statistical model and prior distribution for the true parameter values. The approach takes account of the experimental aim via specification of the utility and of all assumed sources of uncertainty via the expected utility. However, it is predicated on the specification of the statistical model. Recently, a new type of statistical inference, known as Gibbs (or General Bayesian) inference, has been advanced. This is Bayesian-like, in that uncertainty on unknown quantities is represented by a posterior distribution, but does not necessarily rely on specification of a statistical model. Thus the resulting inference should be less sensitive to misspecification of the statistical model. The purpose of this paper is to propose Gibbs optimal design: a framework for optimal design of experiments for Gibbs inference. The concept behind the framework is introduced along with a computational approach to find Gibbs optimal designs in practice. The framework is demonstrated on exemplars including linear models, and experiments with count and time-to-event responses.

Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of initialization and stochastic gradients. With a provable asymptotic guarantee, we present a general stacking framework to make use of all available posterior approximations. Our stacking method is able to combine densities, simulation draws, confidence intervals, and moments, and address the overall precision, calibration, coverage, and bias at the same time. We illustrate our method on several benchmark simulations and a challenging cosmological inference task.

Reinforcement learning suffers from limitations in real practices primarily due to the numbers of required interactions with virtual environments. It results in a challenging problem that we are implausible to obtain an optimal strategy only with a few attempts for many learning method. Hereby, we design an improved reinforcement learning method based on model predictive control that models the environment through a data-driven approach. Based on learned environmental model, it performs multi-step prediction to estimate the value function and optimize the policy. The method demonstrates higher learning efficiency, faster convergent speed of strategies tending to the optimal value, and fewer sample capacity space required by experience replay buffers. Experimental results, both in classic databases and in a dynamic obstacle avoidance scenario for unmanned aerial vehicle, validate the proposed approaches.

Structured reinforcement learning leverages policies with advantageous properties to reach better performance, particularly in scenarios where exploration poses challenges. We explore this field through the concept of orchestration, where a (small) set of expert policies guides decision-making; the modeling thereof constitutes our first contribution. We then establish value-functions regret bounds for orchestration in the tabular setting by transferring regret-bound results from adversarial settings. We generalize and extend the analysis of natural policy gradient in Agarwal et al. [2021, Section 5.3] to arbitrary adversarial aggregation strategies. We also extend it to the case of estimated advantage functions, providing insights into sample complexity both in expectation and high probability. A key point of our approach lies in its arguably more transparent proofs compared to existing methods. Finally, we present simulations for a stochastic matching toy model.

This proposed model introduces novel deep learning methodologies. The objective here is to create a reliable intrusion detection mechanism to help identify malicious attacks. Deep learning based solution framework is developed consisting of three approaches. The first approach is Long-Short Term Memory Recurrent Neural Network (LSTM-RNN) with seven optimizer functions such as adamax, SGD, adagrad, adam, RMSprop, nadam and adadelta. The model is evaluated on NSL-KDD dataset and classified multi attack classification. The model has outperformed with adamax optimizer in terms of accuracy, detection rate and low false alarm rate. The results of LSTM-RNN with adamax optimizer is compared with existing shallow machine and deep learning models in terms of accuracy, detection rate and low false alarm rate. The multi model methodology consisting of Recurrent Neural Network (RNN), Long-Short Term Memory Recurrent Neural Network (LSTM-RNN), and Deep Neural Network (DNN). The multi models are evaluated on bench mark datasets such as KDD99, NSL-KDD, and UNSWNB15 datasets. The models self-learnt the features and classifies the attack classes as multi-attack classification. The models RNN, and LSTM-RNN provide considerable performance compared to other existing methods on KDD99 and NSL-KDD dataset

We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing {\it ad hoc} approach, such as the last value carried forward, is biased. We propose a kernel weighting approach to get an unbiased estimation of the non-parametric coefficient function and establish asymptotic normality for any fixed time point. Furthermore, we construct the simultaneous confidence band to examine the overall magnitude of the variation. Simulation studies support our theoretical predictions and show favorable performance of the proposed method. A data set from cerebral infarction is used to illustrate our methodology.

The present work explores the theoretical limits of Machine Learning (ML) within the framework of Kolmogorov's theory of Algorithmic Probability, which clarifies the notion of entropy as Expected Kolmogorov Complexity and formalizes other fundamental concepts such as Occam's razor via Levin's Universal Distribution. As a fundamental application, we develop Maximum Entropy methods that allow us to derive the Erd\H{o}s--Kac Law and Hardy--Ramanujan theorem in Probabilistic Number Theory, and establish the impossibility of discovering a formula for primes using Machine Learning via the Prime Coding Theorem.

We show that the use of large language models (LLMs) is prevalent among crowd workers, and that targeted mitigation strategies can significantly reduce, but not eliminate, LLM use. On a text summarization task where workers were not directed in any way regarding their LLM use, the estimated prevalence of LLM use was around 30%, but was reduced by about half by asking workers to not use LLMs and by raising the cost of using them, e.g., by disabling copy-pasting. Secondary analyses give further insight into LLM use and its prevention: LLM use yields high-quality but homogeneous responses, which may harm research concerned with human (rather than model) behavior and degrade future models trained with crowdsourced data. At the same time, preventing LLM use may be at odds with obtaining high-quality responses; e.g., when requesting workers not to use LLMs, summaries contained fewer keywords carrying essential information. Our estimates will likely change as LLMs increase in popularity or capabilities, and as norms around their usage change. Yet, understanding the co-evolution of LLM-based tools and users is key to maintaining the validity of research done using crowdsourcing, and we provide a critical baseline before widespread adoption ensues.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.