In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases, statistical measures have been constructed, such as cross validation, information criteria, and marginal likelihood, however, their mathematical properties have not yet been completely clarified when statistical models are under- and over- parametrized. We introduce a place of mathematical theory of Bayesian statistics for unknown uncertainty, which clarifies general properties of cross validation, information criteria, and marginal likelihood, even if an unknown data-generating process is unrealizable by a model or even if the posterior distribution cannot be approximated by any normal distribution. Hence it gives a helpful standpoint for a person who cannot believe in any specific model and prior. This paper consists of three parts. The first is a new result, whereas the second and third are well-known previous results with new experiments. We show there exists a more precise estimator of the generalization loss than leave-one-out cross validation, there exists a more accurate approximation of marginal likelihood than BIC, and the optimal hyperparameters for generalization loss and marginal likelihood are different.

This paper introduces XFL, an industrial-grade federated learning project. XFL supports training AI models collaboratively on multiple devices, while utilizes homomorphic encryption, differential privacy, secure multi-party computation and other security technologies ensuring no leakage of data. XFL provides an abundant algorithms library, integrating a large number of pre-built, secure and outstanding federated learning algorithms, covering both the horizontally and vertically federated learning scenarios. Numerical experiments have shown the prominent performace of these algorithms. XFL builds a concise configuration interfaces with presettings for all federation algorithms, and supports the rapid deployment via docker containers.Therefore, we believe XFL is the most user-friendly and easy-to-develop federated learning framework. XFL is open-sourced, and both the code and documents are available at https://github.com/paritybit-ai/XFL.

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost of evaluating the data likelihood. To alleviate this problem, we consider using Gaussian process regression to build a surrogate model for the likelihood, resulting in an approximate posterior distribution that is amenable to computations in practice. This work serves as an introduction to Gaussian process regression, in particular in the context of building surrogate models for inverse problems, and presents new insights into a suitable choice of training points. We show that the error between the true and approximate posterior distribution can be bounded by the error between the true and approximate likelihood, measured in the $L^2$-norm weighted by the true posterior, and that efficiently bounding the error between the true and approximate likelihood in this norm suggests choosing the training points in the Gaussian process surrogate model based on the true posterior.

Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer, there is a need for efficient methods which can be used to map classical data on quantum states in a concise manner. On the other hand, to verify the results of quantum computers and study quantum algorithms, we need to be able to approximate quantum operations into forms that are easier to simulate on classical computers with some errors. Motivated by these needs, in this paper we study the approximation of matrices and vectors by using their tensor products obtained through successive Schmidt decompositions. We show that data with distributions such as uniform, Poisson, exponential, or similar to these distributions can be approximated by using only a few terms which can be easily mapped onto quantum circuits. The examples include random data with different distributions, the Gram matrices of iris flower, handwritten digits, 20newsgroup, and labeled faces in the wild. And similarly, some quantum operations such as quantum Fourier transform and variational quantum circuits with a small depth also may be approximated with a few terms that are easier to simulate on classical computers. Furthermore, we show how the method can be used to simplify quantum Hamiltonians: In particular, we show the application to randomly generated transverse field Ising model Hamiltonians. The reduced Hamiltonians can be mapped into quantum circuits easily and therefore can be simulated more efficiently.

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method. In addition to the maximum a posteriori (MAP) estimate for the image, which can be obtained with conventional methods, the minimum mean square error (MMSE) estimate and uncertainty maps can also be computed. The data-driven Markov chains are constructed from the generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement. This provides flexibility because the method can be applied to k-space acquired with different sampling schemes or receive coils using the same pre-trained models. Furthermore, we use a framework based on a reverse diffusion process to be able to utilize advanced generative models. The performance of the method is evaluated on an open dataset using 10-fold undersampling in k-space.

Interpretable machine learning offers insights into what factors drive a certain prediction of a black-box system. A large number of interpreting methods focus on identifying explanatory input features, which generally fall into two main categories: attribution and selection. A popular attribution-based approach is to exploit local neighborhoods for learning instance-specific explainers in an additive manner. The process is thus inefficient and susceptible to poorly-conditioned samples. However, they can only interpret single-class predictions and many suffer from inconsistency across different settings, due to a strict reliance on a pre-defined number of features selected. This work exploits the strengths of both methods and proposes a framework for learning local explanations simultaneously for multiple target classes. Our model explainer significantly outperforms additive and instance-wise counterparts on faithfulness with more compact and comprehensible explanations. We also demonstrate the capacity to select stable and important features through extensive experiments on various data sets and black-box model architectures. Black-box machine learning systems enjoy a remarkable predictive performance at the cost of interpretability. This trade-off has motivated a number of interpreting approaches for explaining the behavior of these complex models. Such explanations are particularly useful for high-stakes applications such as healthcare (Caruana et al., 2015; Rich, 2016), cybersecurity (Nguyen et al., 2021) or criminal investigation (Lipton, 2018). While model interpretation can be done in various ways (Mothilal et al., 2020; Bodria et al., 2021), our discussion will focus on feature importance or saliency-based approach - that is, to assign relative importance weights to individual features w.r.t the model's prediction on an input example. Features here refer to input components interpretable to humans; for high-dimensional data such as texts or images, features can be a bag of words/phrases or a group of pixels/super-pixels (Ribeiro et al., 2016). Explanations are generally made by selecting top K features with the highest weights, signifying K most important features to a black-box's decision.

This paper proposes an unsupervised classification method that partitions a set of files into non-overlapping dialects based upon their behaviors, determined by messages produced by a collection of programs that consume them. The pattern of messages can be used as the signature of a particular kind of behavior, with the understanding that some messages are likely to co-occur, while others are not. Patterns of messages can be used to classify files into dialects. A dialect is defined by a subset of messages, called the required messages. Once files are conditioned upon dialect and its required messages, the remaining messages are statistically independent. With this definition of dialect in hand, we present a greedy algorithm that deduces candidate dialects from a dataset consisting of a matrix of file-message data, demonstrate its performance on several file formats, and prove conditions under which it is optimal. We show that an analyst needs to consider fewer dialects than distinct message patterns, which reduces their cognitive load when studying a complex format.

Intention prediction has become a relevant field of research in Human-Machine and Human-Robot Interaction. Indeed, any artificial system (co)-operating with and along humans, designed to assist and coordinate its actions with a human partner, would benefit from first inferring the human's current intention. To spare the user the cognitive burden of explicitly uttering their goals, this inference relies mostly on behavioral cues deemed indicative of the current action. It has been long known that eye movements are highly anticipatory of the single steps unfolding during a task, hence they can serve as a very early and reliable behavioural cue for intention recognition. This review aims to draw a line between insights in the psychological literature on visuomotor control and relevant applications of gaze-based intention recognition in technical domains, with a focus on teleoperated and assistive robotic systems. Starting from the cognitive principles underlying the relationship between intentions, eye movements, and action, the use of eye tracking and gaze-based models for intent recognition in Human-Robot Interaction is considered, with prevalent methodologies and their diverse applications. Finally, special consideration is given to relevant human factors issues and current limitations to be factored in when designing such systems.

Accurate chemical sensors are vital in medical, military, and home safety applications. Training machine learning models to be accurate on real world chemical sensor data requires performing many diverse, costly experiments in controlled laboratory settings to create a data set. In practice even expensive, large data sets may be insufficient for generalization of a trained model to a real-world testing distribution. Rather than perform greater numbers of experiments requiring exhaustive mixtures of chemical analytes, this research proposes learning approximations of complex exposures from training sets of simple ones by using single-analyte exposure signals as building blocks of a multiple-analyte space. We demonstrate this approach to synthetic sensor responses surprisingly improves the detection of out-of-distribution obscured chemical analytes. Further, we pair these synthetic signals to targets in an information-dense representation space utilizing a large corpus of chemistry knowledge. Through utilization of a semantically meaningful analyte representation spaces along with synthetic targets we achieve rapid analyte classification in the presence of obscurants without corresponding obscured-analyte training data. Transfer learning for supervised learning with molecular representations makes assumptions about the input data. Instead, we borrow from the natural language and natural image processing literature for a novel approach to chemical sensor signal classification using molecular semantics for arbitrary chemical sensor hardware designs.

K-means Clustering is the most well-known partitioning algorithm among all clustering, by which we can partition the data objects very easily in to more than one clusters. However, for K-means to choose an appropriate number of clusters without any prior domain knowledge about the dataset is challenging, especially in high-dimensional data objects. Hence, we have implemented the Silhouette and Elbow methods with PCA to find an optimal number of clusters. Also, previously, so many meta-heuristic swarm intelligence algorithms inspired by nature have been employed to handle the automatic data clustering problem. Firefly is efficient and robust for automatic clustering. However, in the Firefly algorithm, the entire population is automatically subdivided into sub-populations that decrease the convergence rate speed and trapping to local minima in high-dimensional optimization problems. Thus, our study proposed an enhanced firefly, i.e., a hybridized K-means with an ODFA model for automatic clustering. The experimental part shows output and graphs of the Silhouette and Elbow methods as well as the Firefly algorithm