We propose a novel Bayesian approach for the adaptive and online estimation of the frequency distribution of a finite number of categories under the local differential privacy (LDP) framework. The proposed algorithm performs Bayesian parameter estimation via posterior sampling and adapts the randomization mechanism for LDP based on the obtained posterior samples. We propose a randomized mechanism for LDP which uses a subset of categories as an input and whose performance depends on the selected subset and the true frequency distribution. By using the posterior sample as an estimate of the frequency distribution, the algorithm performs a computationally tractable subset selection step to maximize the utility of the privatized response of the next user. We propose several utility functions related to well-known information metrics, such as (but not limited to) Fisher information matrix, total variation distance, and information entropy. We compare each of these utility metrics in terms of their computational complexity. We employ stochastic gradient Langevin dynamics for posterior sampling, a computationally efficient approximate Markov chain Monte Carlo method. We provide a theoretical analysis showing that (i) the posterior distribution targeted by the algorithm converges to the true parameter even for approximate posterior sampling, and (ii) the algorithm selects the optimal subset with high probability if posterior sampling is performed exactly. We also provide numerical results that empirically demonstrate the estimation accuracy of our algorithm where we compare it with nonadaptive and semi-adaptive approaches under experimental settings with various combinations of privacy parameters and population distribution parameters.

We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR method naturally combines the principles of Invertible Neural Networks (INNs) and Equation Learner (EQL), a neural network-based symbolic architecture for function learning. In particular, we transform the affine coupling blocks of INNs into a symbolic framework, resulting in an end-to-end differentiable symbolic invertible architecture that allows for efficient gradient-based learning. The proposed ISR framework also relies on sparsity promoting regularization, allowing the discovery of concise and interpretable invertible expressions. We show that ISR can serve as a (symbolic) normalizing flow for density estimation tasks. Furthermore, we highlight its practical applicability in solving inverse problems, including a benchmark inverse kinematics problem, and notably, a geoacoustic inversion problem in oceanography aimed at inferring posterior distributions of underlying seabed parameters from acoustic signals.

In this research, we analyzed the suitability of each of the current state-of-the-art machine learning models for various cyberattack detection from the past 5 years with a major emphasis on the most recent works for comparative study to identify the knowledge gap where work is still needed to be done with regard to detection of each category of cyberattack. We also reviewed the suitability, effeciency and limitations of recent research on state-of-the-art classifiers and novel frameworks in the detection of differnet cyberattacks. Our result shows the need for; further research and exploration on machine learning approach for the detection of drive-by download attacks, an investigation into the mix performance of Naive Bayes to identify possible research direction on improvement to existing state-of-the-art Naive Bayes classifier, we also identify that current machine learning approach to the detection of SQLi attack cannot detect an already compromised database with SQLi attack signifying another possible future research direction.

Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data. Specifically, PPI methods provide tighter confidence intervals by combining small amounts of human-labeled data with larger amounts of data labeled by a reasonably accurate, but potentially biased, automatic system. We propose a framework for PPI based on Bayesian inference that allows researchers to develop new task-appropriate PPI methods easily. Exploiting the ease with which we can design new metrics, we propose improved PPI methods for several importantcases, such as autoraters that give discrete responses (e.g., prompted LLM ``judges'') and autoraters with scores that have a non-linear relationship to human scores.

Cross-domain offline reinforcement learning leverages source domain data with diverse transition dynamics to alleviate the data requirement for the target domain. However, simply merging the data of two domains leads to performance degradation due to the dynamics mismatch. Existing methods address this problem by measuring the dynamics gap via domain classifiers while relying on the assumptions of the transferability of paired domains. In this paper, we propose a novel representation-based approach to measure the domain gap, where the representation is learned through a contrastive objective by sampling transitions from different domains. We show that such an objective recovers the mutual-information gap of transition functions in two domains without suffering from the unbounded issue of the dynamics gap in handling significantly different domains. Based on the representations, we introduce a data filtering algorithm that selectively shares transitions from the source domain according to the contrastive score functions. Empirical results on various tasks demonstrate that our method achieves superior performance, using only 10% of the target data to achieve 89.2% of the performance on 100% target dataset with state-of-the-art methods.

We introduce a novel multi-armed bandit framework, where each arm is associated with a fixed unknown credal set over the space of outcomes (which can be richer than just the reward). The arm-to-credal-set correspondence comes from a known class of hypotheses. We then define a notion of regret corresponding to the lower prevision defined by these credal sets. Equivalently, the setting can be regarded as a two-player zero-sum game, where, on each round, the agent chooses an arm and the adversary chooses the distribution over outcomes from a set of options associated with this arm. The regret is defined with respect to the value of game. For certain natural hypothesis classes, loosely analgous to stochastic linear bandits (which are a special case of the resulting setting), we propose an algorithm and prove a corresponding upper bound on regret. We also prove lower bounds on regret for particular special cases.

There have been many applications of deep neural networks to detector calibrations and a growing number of studies that propose deep generative models as automated fast detector simulators. We show that these two tasks can be unified by using maximum likelihood estimation (MLE) from conditional generative models for energy regression. Unlike direct regression techniques, the MLE approach is prior-independent and non-Gaussian resolutions can be determined from the shape of the likelihood near the maximum. Using an ATLAS-like calorimeter simulation, we demonstrate this concept in the context of calorimeter energy calibration.

Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art Markov chain Monte Carlo technique, exploiting the shape of such high-dimensional target distributions to efficiently generate samples. Despite its impressive empirical success and increasing popularity, its wide-scale adoption remains limited due to the high computational cost of gradient calculation. Moreover, applying this method is impossible when the gradient of the posterior cannot be computed (for example, with black-box simulators). To overcome these challenges, we propose a novel two-stage Hamiltonian Monte Carlo algorithm with a surrogate model. In this multi-fidelity algorithm, the acceptance probability is computed in the first stage via a standard HMC proposal using an inexpensive differentiable surrogate model, and if the proposal is accepted, the posterior is evaluated in the second stage using the high-fidelity (HF) numerical solver. Splitting the standard HMC algorithm into these two stages allows for approximating the gradient of the posterior efficiently, while producing accurate posterior samples by using HF numerical solvers in the second stage. We demonstrate the effectiveness of this algorithm for a range of problems, including linear and nonlinear Bayesian inverse problems with in-silico data and experimental data. The proposed algorithm is shown to seamlessly integrate with various low-fidelity and HF models, priors, and datasets. Remarkably, our proposed method outperforms the traditional HMC algorithm in both computational and statistical efficiency by several orders of magnitude, all while retaining or improving the accuracy in computed posterior statistics.

We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The notion of data separability is not needed, which is in contrast to the classical set up of multi-class logistic regression in which each data sample belongs to one class. We also provide a general and constructive estimate of the convergence rate to the maximum likelihood estimate when gradient descent is used as the optimizer. Our estimate involves bounding the condition number of the Hessian of the maximum likelihood function. The approaches used in this article rely on a simple operator-theoretic framework.

Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the $\textit{exclusion criterion}$, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides $\textit{partial}$ identification in linear systems given a set of $\textit{leaky instruments}$, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art. An accompanying $\texttt{R}$ package, $\texttt{leakyIV}$, is available from $\texttt{CRAN}$.