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Aggregate measures of family planning are used to monitor demand for and usage of contraceptive methods in populations globally, for example as part of the FP2030 initiative. Family planning measures for low- and middle-income countries are typically based on data collected through cross-sectional household surveys. Recently proposed measures account for sexual activity through assessment of the distribution of time-between-sex (TBS) in the population of interest. In this paper, we propose a statistical approach to estimate the distribution of TBS using data typically available in low- and middle-income countries, while addressing two major challenges. The first challenge is that timing of sex information is typically limited to women's time-since-last-sex (TSLS) data collected in the cross-sectional survey. In our proposed approach, we adopt the current duration method to estimate the distribution of TBS using the available TSLS data, from which the frequency of sex at the population level can be derived. Furthermore, the observed TSLS data are subject to reporting issues because they can be reported in different units and may be rounded off. To apply the current duration approach and account for these data reporting issues, we develop a flexible Bayesian model, and provide a detailed technical description of the proposed modeling approach.

We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD). We show numerical error (on the order of the smallest floating point bit) induced from floating point arithmetic in training deep nets can be amplified significantly and result in significant test accuracy variance, comparable to the test accuracy variance due to stochasticity in SGD. We show how this is likely traced to instabilities of the optimization dynamics that are restrained, i.e., localized over iterations and regions of the weight tensor space. We do this by presenting a theoretical framework using numerical analysis of partial differential equations (PDE), and analyzing the gradient descent PDE of convolutional neural networks (CNNs). We show that it is stable only under certain conditions on the learning rate and weight decay. We show that rather than blowing up when the conditions are violated, the instability can be restrained. We show this is a consequence of the non-linear PDE associated with the gradient descent of the CNN, whose local linearization changes when over-driving the step size of the discretization, resulting in a stabilizing effect. We link restrained instabilities to the recently discovered Edge of Stability (EoS) phenomena, in which the stable step size predicted by classical theory is exceeded while continuing to optimize the loss and still converging. Because restrained instabilities occur at the EoS, our theory provides new predictions about the EoS, in particular, the role of regularization and the dependence on the network complexity.

This thesis focuses on the advancement of probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random variables, which is necessary for applications with numeric data. The first contribution is the introduction of context-specific likelihood weighting (CS-LW), a new sampling algorithm that exploits context-specific independencies for computational gains. Next, a new hybrid PLP, DC#, is introduced, which integrates the syntax of Distributional Clauses with Bayesian logic programs and represents three types of independencies: i) conditional independencies (CIs) modeled in Bayesian networks; ii) context-specific independencies (CSIs) represented by logical rules, and iii) independencies amongst attributes of related objects in relational models expressed by combining rules. The scalable inference algorithm FO-CS-LW is introduced for DC#. Finally, the thesis addresses the lack of approaches for learning hybrid PLP from relational data and background knowledge with the introduction of DiceML, which learns the structure and parameters of hybrid PLP and tackles the relational autocompletion problem. The conclusion discusses future directions and open challenges for hybrid PLP.

Improving road safety is hugely important with the number of deaths on the world's roads remaining unacceptably high; an estimated 1.35 million people die each year (WHO, 2020). Current practice for treating collision hotspots is almost always reactive: once a threshold level of collisions has been exceeded during some predetermined observation period, treatment is applied (e.g. road safety cameras). However, more recently, methodology has been developed to predict collision counts at potential hotspots in future time periods, with a view to a more proactive treatment of road safety hotspots. Dynamic linear models provide a flexible framework for predicting collisions and thus enabling such a proactive treatment. In this paper, we demonstrate how such models can be used to capture both seasonal variability and spatial dependence in time course collision rates at several locations. The model allows for within- and out-of-sample forecasting for locations which are fully observed and for locations where some data are missing. We illustrate our approach using collision rate data from 8 Traffic Administration Zones in North Florida, USA, and find that the model provides a good description of the underlying process and reasonable forecast accuracy.

This paper considers the problem of estimating the distribution of a response variable conditioned on observing some factors. Existing approaches are often deficient in one of the qualities of flexibility, interpretability and tractability. We propose a model that possesses these desirable properties. The proposed model, analogous to classic mixture regression models, models the conditional quantile function as a mixture (weighted sum) of basis quantile functions, with the weight of each basis quantile function being a function of the factors. The model can approximate any bounded conditional quantile model. It has a factor model structure with a closed-form expression. The calibration problem is formulated as convex optimization, which can be viewed as conducting quantile regressions of all confidence levels simultaneously and does not suffer from quantile crossing by design. The calibration is equivalent to minimization of Continuous Probability Ranked Score (CRPS). We prove the asymptotic normality of the estimator. Additionally, based on risk quadrangle framework, we generalize the proposed approach to conditional distributions defined by Conditional Value-at-Risk (CVaR), expectile and other functions of uncertainty measures. Based on CP decomposition of tensors, we propose a dimensionality reduction method by reducing the rank of the parameter tensor and propose an alternating algorithm for estimating the parameter tensor. Our numerical experiments demonstrate the efficiency of the approach.

The adoption of deep neural networks (DNNs) in safety-critical contexts is often prevented by the lack of effective means to explain their results, especially when they are erroneous. In our previous work, we proposed a white-box approach (HUDD) and a black-box approach (SAFE) to automatically characterize DNN failures. They both identify clusters of similar images from a potentially large set of images leading to DNN failures. However, the analysis pipelines for HUDD and SAFE were instantiated in specific ways according to common practices, deferring the analysis of other pipelines to future work. In this paper, we report on an empirical evaluation of 99 different pipelines for root cause analysis of DNN failures. They combine transfer learning, autoencoders, heatmaps of neuron relevance, dimensionality reduction techniques, and different clustering algorithms. Our results show that the best pipeline combines transfer learning, DBSCAN, and UMAP. It leads to clusters almost exclusively capturing images of the same failure scenario, thus facilitating root cause analysis. Further, it generates distinct clusters for each root cause of failure, thus enabling engineers to detect all the unsafe scenarios. Interestingly, these results hold even for failure scenarios that are only observed in a small percentage of the failing images.

Effective evaluation methods remain a significant challenge for research on open-domain conversational dialogue systems. Explicit satisfaction ratings can be elicited from users, but users often do not provide ratings when asked, and those they give can be highly subjective. Post-hoc ratings by experts are an alternative, but these can be both expensive and complex to collect. Here, we explore the creation of automated methods for predicting both expert and user ratings of open-domain dialogues. We compare four different approaches. First, we train a baseline model using an end-to-end transformer to predict ratings directly from the raw dialogue text. The other three methods are variants of a two-stage approach in which we first extract interpretable features at the turn level that capture, among other aspects, user dialogue behaviors indicating contradiction, repetition, disinterest, compliments, or criticism. We project these features to the dialogue level and train a dialogue-level MLP regression model, a dialogue-level LSTM, and a novel causal inference model called counterfactual-LSTM (CF-LSTM) to predict ratings. The proposed CF-LSTM is a sequential model over turn-level features which predicts ratings using multiple regressors depending on hypotheses derived from the turn-level features. As a causal inference model, CF-LSTM aims to learn the underlying causes of a specific event, such as a low rating. We also bin the user ratings and perform classification experiments with all four models. In evaluation experiments on conversational data from the Alexa Prize SocialBot, we show that the CF-LSTM achieves the best performance for predicting dialogue ratings and classification.

Interpretability methods are developed to understand the working mechanisms of black-box models, which is crucial to their responsible deployment. Fulfilling this goal requires both that the explanations generated by these methods are correct and that people can easily and reliably understand them. While the former has been addressed in prior work, the latter is often overlooked, resulting in informal model understanding derived from a handful of local explanations. In this paper, we introduce explanation summary (ExSum), a mathematical framework for quantifying model understanding, and propose metrics for its quality assessment. On two domains, ExSum highlights various limitations in the current practice, helps develop accurate model understanding, and reveals easily overlooked properties of the model. We also connect understandability to other properties of explanations such as human alignment, robustness, and counterfactual minimality and plausibility.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.