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Bundle Adjustment (BA) refers to the problem of simultaneous determination of sensor poses and scene geometry, which is a fundamental problem in robot vision. This paper presents an efficient and consistent bundle adjustment method for lidar sensors. The method employs edge and plane features to represent the scene geometry, and directly minimizes the natural Euclidean distance from each raw point to the respective geometry feature. A nice property of this formulation is that the geometry features can be analytically solved, drastically reducing the dimension of the numerical optimization. To represent and solve the resultant optimization problem more efficiently, this paper then proposes a novel concept {\it point clusters}, which encodes all raw points associated to the same feature by a compact set of parameters, the {\it point cluster coordinates}. We derive the closed-form derivatives, up to the second order, of the BA optimization based on the point cluster coordinates and show their theoretical properties such as the null spaces and sparsity. Based on these theoretical results, this paper develops an efficient second-order BA solver. Besides estimating the lidar poses, the solver also exploits the second order information to estimate the pose uncertainty caused by measurement noises, leading to consistent estimates of lidar poses. Moreover, thanks to the use of point cluster, the developed solver fundamentally avoids the enumeration of each raw point (which is very time-consuming due to the large number) in all steps of the optimization: cost evaluation, derivatives evaluation and uncertainty evaluation. The implementation of our method is open sourced to benefit the robotics community and beyond.

High-quality medical systematic reviews require comprehensive literature searches to ensure the recommendations and outcomes are sufficiently reliable. Indeed, searching for relevant medical literature is a key phase in constructing systematic reviews and often involves domain (medical researchers) and search (information specialists) experts in developing the search queries. Queries in this context are highly complex, based on Boolean logic, include free-text terms and index terms from standardised terminologies (e.g., the Medical Subject Headings (MeSH) thesaurus), and are difficult and time-consuming to build. The use of MeSH terms, in particular, has been shown to improve the quality of the search results. However, identifying the correct MeSH terms to include in a query is difficult: information experts are often unfamiliar with the MeSH database and unsure about the appropriateness of MeSH terms for a query. Naturally, the full value of the MeSH terminology is often not fully exploited. This article investigates methods to suggest MeSH terms based on an initial Boolean query that includes only free-text terms. In this context, we devise lexical and pre-trained language models based methods. These methods promise to automatically identify highly effective MeSH terms for inclusion in a systematic review query. Our study contributes an empirical evaluation of several MeSH term suggestion methods. We further contribute an extensive analysis of MeSH term suggestions for each method and how these suggestions impact the effectiveness of Boolean queries.

In this paper, I develop a formula for estimating Bayes factors directly from minimal summary statistics produced in repeated measures analysis of variance designs. The formula, which requires knowing only the $F$-statistic, the number of subjects, and the number of repeated measurements per subject, is based on the BIC approximation of the Bayes factor, a common default method for Bayesian computation with linear models. In addition to providing computational examples, I report a simulation study in which I demonstrate that the formula compares favorably to a recently developed, more complex method that accounts for correlation between repeated measurements. The minimal BIC method provides a simple way for researchers to estimate Bayes factors from a minimal set of summary statistics, giving users a powerful index for estimating the evidential value of not only their own data, but also the data reported in published studies.

We propose a symbolic execution method for programs that can draw random samples. In contrast to existing work, our method can verify randomized programs with unknown inputs and can prove probabilistic properties that universally quantify over all possible inputs. Our technique augments standard symbolic execution with a new class of \emph{probabilistic symbolic variables}, which represent the results of random draws, and computes symbolic expressions representing the probability of taking individual paths. We implement our method on top of the \textsc{KLEE} symbolic execution engine alongside multiple optimizations and use it to prove properties about probabilities and expected values for a range of challenging case studies written in C++, including Freivalds' algorithm, randomized quicksort, and a randomized property-testing algorithm for monotonicity. We evaluate our method against \textsc{Psi}, an exact probabilistic symbolic inference engine, and \textsc{Storm}, a probabilistic model checker, and show that our method significantly outperforms both tools.

QBF solvers implementing the QCDCL paradigm are powerful algorithms that successfully tackle many computationally complex applications. However, our theoretical understanding of the strength and limitations of these QCDCL solvers is very limited. In this paper we suggest to formally model QCDCL solvers as proof systems. We define different policies that can be used for decision heuristics and unit propagation and give rise to a number of sound and complete QBF proof systems (and hence new QCDCL algorithms). With respect to the standard policies used in practical QCDCL solving, we show that the corresponding QCDCL proof system is incomparable (via exponential separations) to Q-resolution, the classical QBF resolution system used in the literature. This is in stark contrast to the propositional setting where CDCL and resolution are known to be p-equivalent. This raises the question what formulas are hard for standard QCDCL, since Q-resolution lower bounds do not necessarily apply to QCDCL as we show here. In answer to this question we prove several lower bounds for QCDCL, including exponential lower bounds for a large class of random QBFs. We also introduce a strengthening of the decision heuristic used in classical QCDCL, which does not necessarily decide variables in order of the prefix, but still allows to learn asserting clauses. We show that with this decision policy, QCDCL can be exponentially faster on some formulas. We further exhibit a QCDCL proof system that is p-equivalent to Q-resolution. In comparison to classical QCDCL, this new QCDCL version adapts both decision and unit propagation policies.

We consider the stochastic gradient descent (SGD) algorithm driven by a general stochastic sequence, including i.i.d noise and random walk on an arbitrary graph, among others; and analyze it in the asymptotic sense. Specifically, we employ the notion of `efficiency ordering', a well-analyzed tool for comparing the performance of Markov Chain Monte Carlo (MCMC) samplers, for SGD algorithms in the form of Loewner ordering of covariance matrices associated with the scaled iterate errors in the long term. Using this ordering, we show that input sequences that are more efficient for MCMC sampling also lead to smaller covariance of the errors for SGD algorithms in the limit. This also suggests that an arbitrarily weighted MSE of SGD iterates in the limit becomes smaller when driven by more efficient chains. Our finding is of particular interest in applications such as decentralized optimization and swarm learning, where SGD is implemented in a random walk fashion on the underlying communication graph for cost issues and/or data privacy. We demonstrate how certain non-Markovian processes, for which typical mixing-time based non-asymptotic bounds are intractable, can outperform their Markovian counterparts in the sense of efficiency ordering for SGD. We show the utility of our method by applying it to gradient descent with shuffling and mini-batch gradient descent, reaffirming key results from existing literature under a unified framework. Empirically, we also observe efficiency ordering for variants of SGD such as accelerated SGD and Adam, open up the possibility of extending our notion of efficiency ordering to a broader family of stochastic optimization algorithms.

The prevalence of employing attention mechanisms has brought along concerns on the interpretability of attention distributions. Although it provides insights about how a model is operating, utilizing attention as the explanation of model predictions is still highly dubious. The community is still seeking more interpretable strategies for better identifying local active regions that contribute the most to the final decision. To improve the interpretability of existing attention models, we propose a novel Bilinear Representative Non-Parametric Attention (BR-NPA) strategy that captures the task-relevant human-interpretable information. The target model is first distilled to have higher-resolution intermediate feature maps. From which, representative features are then grouped based on local pairwise feature similarity, to produce finer-grained, more precise attention maps highlighting task-relevant parts of the input. The obtained attention maps are ranked according to the activity level of the compound feature, which provides information regarding the important level of the highlighted regions. The proposed model can be easily adapted in a wide variety of modern deep models, where classification is involved. Extensive quantitative and qualitative experiments showcase more comprehensive and accurate visual explanations compared to state-of-the-art attention models and visualizations methods across multiple tasks including fine-grained image classification, few-shot classification, and person re-identification, without compromising the classification accuracy. The proposed visualization model sheds imperative light on how neural networks `pay their attention' differently in different tasks.

We study the security of Probabilistic Data Structures (PDS) for handling Approximate Membership Queries (AMQ); prominent examples of AMQ-PDS are Bloom and Cuckoo filters. AMQ-PDS are increasingly being deployed in environments where adversaries can gain benefit from carefully selecting inputs, for example to increase the false positive rate of an AMQ-PDS. They are also being used in settings where the inputs are sensitive and should remain private in the face of adversaries who can access an AMQ-PDS through an API or who can learn its internal state by compromising the system running the AMQ-PDS. We develop simulation-based security definitions that speak to correctness and privacy of AMQ-PDS. Our definitions are general and apply to a broad range of adversarial settings. We use our definitions to analyse the behaviour of both Bloom filters and insertion-only Cuckoo filters. We show that these AMQ-PDS can be provably protected through replacement or composition of hash functions with keyed pseudorandom functions in their construction. We also examine the practical impact on storage size and computation of providing secure instances of Bloom and insertion-only Cuckoo filters.

Transparency in Machine Learning (ML), attempts to reveal the working mechanisms of complex models. Transparent ML promises to advance human factors engineering goals of human-centered AI in the target users. From a human-centered design perspective, transparency is not a property of the ML model but an affordance, i.e. a relationship between algorithm and user; as a result, iterative prototyping and evaluation with users is critical to attaining adequate solutions that afford transparency. However, following human-centered design principles in healthcare and medical image analysis is challenging due to the limited availability of and access to end users. To investigate the state of transparent ML in medical image analysis, we conducted a systematic review of the literature. Our review reveals multiple severe shortcomings in the design and validation of transparent ML for medical image analysis applications. We find that most studies to date approach transparency as a property of the model itself, similar to task performance, without considering end users during neither development nor evaluation. Additionally, the lack of user research, and the sporadic validation of transparency claims put contemporary research on transparent ML for medical image analysis at risk of being incomprehensible to users, and thus, clinically irrelevant. To alleviate these shortcomings in forthcoming research while acknowledging the challenges of human-centered design in healthcare, we introduce the INTRPRT guideline, a systematic design directive for transparent ML systems in medical image analysis. The INTRPRT guideline suggests formative user research as the first step of transparent model design to understand user needs and domain requirements. Following this process produces evidence to support design choices, and ultimately, increases the likelihood that the algorithms afford transparency.

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.