Lifted inference scales to large probability models by exploiting symmetry. However, existing exact lifted inference techniques do not apply to general factor graphs, as they require a relational representation. In this work we provide a theoretical framework and algorithm for performing exact lifted inference on symmetric factor graphs by computing colored graph automorphisms, as is often done for approximate lifted inference. Our key insight is to represent variable assignments directly in the colored factor graph encoding. This allows us to generate representatives and compute the size of each orbit of the symmetric distribution. In addition to exact inference, we use this encoding to implement an MCMC algorithm that explores the space of orbits quickly by uniform orbit sampling.

Gaussian processes (GP) are a popular Bayesian approach for the optimization of black-box functions. Despite their effectiveness in simple problems, GP-based algorithms hardly scale to complex high-dimensional functions, as their per-iteration time and space cost is at least quadratic in the number of dimensions $d$ and iterations $t$. Given a set of $A$ alternative to choose from, the overall runtime $O(t^3A)$ quickly becomes prohibitive. In this paper, we introduce BKB (budgeted kernelized bandit), a novel approximate GP algorithm for optimization under bandit feedback that achieves near-optimal regret (and hence near-optimal convergence rate) with near-constant per-iteration complexity and no assumption on the input space or covariance of the GP. Combining a kernelized linear bandit algorithm (GP-UCB) with randomized matrix sketching technique (i.e., leverage score sampling), we prove that selecting inducing points based on their posterior variance gives an accurate low-rank approximation of the GP, preserving variance estimates and confidence intervals. As a consequence, BKB does not suffer from variance starvation, an important problem faced by many previous sparse GP approximations. Moreover, we show that our procedure selects at most $\tilde{O}(d_{eff})$ points, where $d_{eff}$ is the effective dimension of the explored space, which is typically much smaller than both $d$ and $t$. This greatly reduces the dimensionality of the problem, thus leading to a $O(TAd_{eff}^2)$ runtime and $O(A d_{eff})$ space complexity.

Markov chain Monte Carlo (MCMC) algorithms are widely used to sample from complicated distributions, especially to sample from the posterior distribution in Bayesian inference. However, MCMC is not directly applicable when facing the doubly intractable problem. In this paper, we discussed and compared two existing solutions -- Pseudo-marginal Monte Carlo and Exchange Algorithm. This paper also proposes a novel algorithm: Multi-armed Bandit MCMC (MABMC), which chooses between two (or more) randomized acceptance ratios in each step. MABMC could be applied directly to incorporate Pseudo-marginal Monte Carlo and Exchange algorithm, with higher average acceptance probability.

One of the biggest challenges in the field of biomedical imaging is the comprehension and the exploitation of the photon scattering through disordered media. Many studies have pursued the solution to this puzzle, achieving light-focusing control or reconstructing images in complex media. In the present work, we investigate how statistical inference helps the calculation of the transmission matrix in a complex scrambling environment, enabling its usage like a normal optical element. We convert a linear input-output transmission problem into a statistical formulation based on pseudolikelihood maximization, learning the coupling matrix via random sampling of intensity realizations. Our aim is to uncover insights from the scattering problem, encouraging the development of novel imaging techniques for better medical investigations, borrowing a number of statistical tools from spin-glass theory.

Phishing as one of the most well-known cybercrime activities is a deception of online users to steal their personal or confidential information by impersonating a legitimate website. Several machine learning-based strategies have been proposed to detect phishing websites. These techniques are dependent on the features extracted from the website samples. However, few studies have actually considered efficient feature selection for detecting phishing attacks. In this work, we investigate an agreement on the definitive features which should be used in phishing detection. We apply Fuzzy Rough Set (FRS) theory as a tool to select most effective features from three benchmarked data sets. The selected features are fed into three often used classifiers for phishing detection. To evaluate the FRS feature selection in developing a generalizable phishing detection, the classifiers are trained by a separate out-of-sample data set of 14,000 website samples. The maximum F-measure gained by FRS feature selection is 95% using Random Forest classification. Also, there are 9 universal features selected by FRS over all the three data sets. The F-measure value using this universal feature set is approximately 93% which is a comparable result in contrast to the FRS performance. Since the universal feature set contains no features from third-part services, this finding implies that with no inquiry from external sources, we can gain a faster phishing detection which is also robust toward zero-day attacks.

Word meaning changes over time, depending on linguistic and extra-linguistic factors. Associating a word's correct meaning in its historical context is a critical challenge in diachronic research, and is relevant to a range of NLP tasks, including information retrieval and semantic search in historical texts. Bayesian models for semantic change have emerged as a powerful tool to address this challenge, providing explicit and interpretable representations of semantic change phenomena. However, while corpora typically come with rich metadata, existing models are limited by their inability to exploit contextual information (such as text genre) beyond the document time-stamp. This is particularly critical in the case of ancient languages, where lack of data and long diachronic span make it harder to draw a clear distinction between polysemy and semantic change, and current systems perform poorly on these languages. We develop GASC, a dynamic semantic change model that leverages categorical metadata about the texts' genre information to boost inference and uncover the evolution of meanings in Ancient Greek corpora. In a new evaluation framework, we show that our model achieves improved predictive performance compared to the state of the art.

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators suited to the experiment design context by building on ideas from variational inference and mutual information estimation. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We demonstrate the practicality of our approach via a number of experiments, including an adaptive experiment with human participants.

In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a generalization of Gaussian random vectors and are associated with the development of kernel methods. Bayesian optimization is an approach for performing derivative-free global optimization in a small dimension, and uses Gaussian processes to locate the global maximum of a black-box function. The first part of the article reviews these two tools and shows how they are connected. In particular, we focus on the Gaussian process regression, which is the core of Bayesian machine learning, and the issue of hyperparameter selection. The second part is dedicated to two financial applications. We first consider the modeling of the term structure of interest rates. More precisely, we test the fitting method and compare the GP prediction and the random walk model. The second application is the construction of trend-following strategies, in particular the online estimation of trend and covariance windows.

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.

Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple variables. We focus on discrete data and propose a new test based on the notion of algorithmic independence that we instantiate using stochastic complexity. Amongst others, we show that our proposed test, SCI, is an asymptotically unbiased as well as $L_2$ consistent estimator for conditional mutual information (CMI). Further, we show that SCI can be reformulated to find a sensible threshold for CMI that works well on limited samples. Empirical evaluation shows that SCI has a lower type II error than commonly used tests. As a result, we obtain a higher recall when we use SCI in causal discovery algorithms, without compromising the precision.