Alzheimer's Disease is a neurodegenerative condition characterized by dementia and impairment in neurological function. The study primarily focuses on the individuals above age 40, affecting their memory, behavior, and cognitive processes of the brain. Alzheimer's disease requires diagnosis by a detailed assessment of MRI scans and neuropsychological tests of the patients. This project compares existing deep learning models in the pursuit of enhancing the accuracy and efficiency of AD diagnosis, specifically focusing on the Convolutional Neural Network, Bayesian Convolutional Neural Network, and the U-net model with the Open Access Series of Imaging Studies brain MRI dataset. Besides, to ensure robustness and reliability in the model evaluations, we address the challenge of imbalance in data. We then perform rigorous evaluation to determine strengths and weaknesses for each model by considering sensitivity, specificity, and computational efficiency. This comparative analysis would shed light on the future role of AI in revolutionizing AD diagnostics but also paved ways for future innovation in medical imaging and the management of neurodegenerative diseases.

Parameter estimation is a fundamental challenge in machine learning, crucial for tasks such as neural network weight fitting and Bayesian inference. This paper focuses on the complexity of estimating translation $\boldsymbol{\mu} \in \mathbb{R}^l$ and shrinkage $\sigma \in \mathbb{R}_{++}$ parameters for a distribution of the form $\frac{1}{\sigma^l} f_0 \left( \frac{\boldsymbol{x} - \boldsymbol{\mu}}{\sigma} \right)$, where $f_0$ is a known density in $\mathbb{R}^l$ given $n$ samples. We highlight that while the problem is NP-hard for Maximum Likelihood Estimation (MLE), it is possible to obtain $\varepsilon$-approximations for arbitrary $\varepsilon > 0$ within $\text{poly} \left( \frac{1}{\varepsilon} \right)$ time using the Wasserstein distance.

Numerous studies have compared machine learning (ML) and discrete choice models (DCMs) in predicting travel demand. However, these studies often lack generalizability as they compare models deterministically without considering contextual variations. To address this limitation, our study develops an empirical benchmark by designing a tournament model, thus efficiently summarizing a large number of experiments, quantifying the randomness in model comparisons, and using formal statistical tests to differentiate between the model and contextual effects. This benchmark study compares two large-scale data sources: a database compiled from literature review summarizing 136 experiments from 35 studies, and our own experiment data, encompassing a total of 6,970 experiments from 105 models and 12 model families. This benchmark study yields two key findings. Firstly, many ML models, particularly the ensemble methods and deep learning, statistically outperform the DCM family (i.e., multinomial, nested, and mixed logit models). However, this study also highlights the crucial role of the contextual factors (i.e., data sources, inputs and choice categories), which can explain models' predictive performance more effectively than the differences in model types alone. Model performance varies significantly with data sources, improving with larger sample sizes and lower dimensional alternative sets. After controlling all the model and contextual factors, significant randomness still remains, implying inherent uncertainty in such model comparisons. Overall, we suggest that future researchers shift more focus from context-specific model comparisons towards examining model transferability across contexts and characterizing the inherent uncertainty in ML, thus creating more robust and generalizable next-generation travel demand models.

In geotechnical engineering, constitutive models play a crucial role in describing soil behavior under varying loading conditions. Data-driven deep learning (DL) models offer a promising alternative for developing predictive constitutive models. When prediction is the primary focus, quantifying the predictive uncertainty of a trained DL model and communicating this uncertainty to end users is crucial for informed decision-making. This study proposes a recursive Bayesian neural network (rBNN) framework, which builds upon recursive feedforward neural networks (rFFNNs) by introducing generalized Bayesian inference for uncertainty quantification. A significant contribution of this work is the incorporation of a sliding window approach in rFFNNs, allowing the models to effectively capture temporal dependencies across load steps. The rBNN extends this framework by treating model parameters as random variables, with their posterior distributions inferred using generalized variational inference. The proposed framework is validated on two datasets: (i) a numerically simulated consolidated drained (CD) triaxial dataset employing a hardening soil model and (ii) an experimental dataset comprising 28 CD triaxial tests on Baskarp sand. Comparative analyses with LSTM, Bi-LSTM, and GRU models demonstrate that the deterministic rFFNN achieves superior predictive accuracy, attributed to its transparent structure and sliding window design. While the rBNN marginally trails in accuracy for the experimental case, it provides robust confidence intervals, addressing data sparsity and measurement noise in experimental conditions. The study underscores the trade-offs between deterministic and probabilistic approaches and the potential of rBNNs for uncertainty-aware constitutive modeling.

The field of Knowledge Tracing is focused on predicting the success rate of a student for a given skill. Modern methods like Deep Knowledge Tracing provide accurate estimates given enough data, but being based on neural networks they struggle to explain how these estimates are formed. More classical methods like Dynamic Bayesian Networks can do this, but they cannot give data on the accuracy of their estimates and often struggle to incorporate new observations in real-time due to their high computational load. This paper presents a novel method, Performance Distribution Tracing (PDT), in which the distribution of the success rate is traced live. It uses a Dynamic Bayesian Network with continuous random variables as nodes. By tracing the success rate distribution, there is always data available on the accuracy of any success rate estimation. In addition, it makes it possible to combine data from similar/related skills to come up with a more informed estimate of success rates. This makes it possible to predict exercise success rates, providing both explainability and an accuracy indication, even when an exercise requires a combination of different skills to solve. And through the use of the beta distribution functions as conjugate priors, all distributions are available in analytical form, allowing efficient online updates upon new observations. Experiments have shown that the resulting estimates generally feel sufficiently accurate to end-users such that they accept recommendations based on them.

Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture models is computationally challenging due to issues such as high-dimensional posterior inference and label switching. Furthermore, traditional methods such as MCMC are applicable only if the likelihoods for each mixture component are analytically tractable. Amortized Bayesian Inference (ABI) is a simulation-based framework for estimating Bayesian models using generative neural networks. This allows the fitting of models without explicit likelihoods, and provides fast inference. ABI is therefore an attractive framework for estimating mixture models. This paper introduces a novel extension of ABI tailored to mixture models. We factorize the posterior into a distribution of the parameters and a distribution of (categorical) mixture indicators, which allows us to use a combination of generative neural networks for parameter inference, and classification networks for mixture membership identification. The proposed framework accommodates both independent and dependent mixture models, enabling filtering and smoothing. We validate and demonstrate our approach through synthetic and real-world datasets.

The covariance matrix is a foundation in numerous statistical and machine-learning applications such as Principle Component Analysis, Correlation Heatmap, etc. However, missing values within datasets present a formidable obstacle to accurately estimating this matrix. While imputation methods offer one avenue for addressing this challenge, they often entail a trade-off between computational efficiency and estimation accuracy. Consequently, attention has shifted towards direct parameter estimation, given its precision and reduced computational burden. In this paper, we propose Direct Parameter Estimation for Randomly Missing Data with Categorical Features (DPERC), an efficient approach for direct parameter estimation tailored to mixed data that contains missing values within continuous features. Our method is motivated by leveraging information from categorical features, which can significantly enhance covariance matrix estimation for continuous features. Our approach effectively harnesses the information embedded within mixed data structures. Through comprehensive evaluations of diverse datasets, we demonstrate the competitive performance of DPERC compared to various contemporary techniques. In addition, we also show by experiments that DPERC is a valuable tool for visualizing the correlation heatmap.

Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy desired constraints or exhibit desired properties is difficult. In practice, expensive heuristic search or reinforcement learning algorithms are often employed. In this paper, we investigate the use of conditional generative models which directly attack this inverse problem, by modeling the distribution of discrete structures given properties of interest. Unfortunately, the maximum likelihood training of such models often fails with the samples from the generative model inadequately respecting the input properties.

To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upward-downward Gibbs sampler, each iteration of which upward samples Dirichlet distributed connection weight vectors starting from the first layer (bottom data layer), and then downward samples gamma distributed hidden units starting from the top hidden layer. The gamma-negative binomial process combined with a layer-wise training strategy allows the PGBN to infer the width of each layer given a fixed budget on the width of the first layer. The PGBN with a single hidden layer reduces to Poisson factor analysis. Example results on text analysis illustrate interesting relationships between the width of the first layer and the inferred network structure, and demonstrate that the PGBN, whose hidden units are imposed with correlated gamma priors, can add more layers to increase its performance gains over Poisson factor analysis, given the same limit on the width of the first layer.

In large-scale systems, complex internal relationships are often present. Such interconnected systems can be effectively described by low rank stochastic processes. When identifying a predictive model of low rank processes from sampling data, the rank-deficient property of spectral densities is often obscured by the inevitable measurement noise in practice. However, existing low rank identification approaches often did not take noise into explicit consideration, leading to non-negligible inaccuracies even under weak noise. In this paper, we address the identification issue of low rank processes under measurement noise. We find that the noisy measurement model admits a sparse plus low rank structure in latent-variable graphical models. Specifically, we first decompose the problem into a maximum entropy covariance extension problem, and a low rank graphical estimation problem based on an autoregressive moving-average with exogenous input (ARMAX) model. To identify the ARMAX low rank graphical models, we propose an estimation approach based on maximum likelihood. The identifiability and consistency of this approach are proven under certain conditions. Simulation results confirm the reliable performance of the entire algorithm in both the parameter estimation and noisy data filtering.