Unimodality, pivotal in statistical analysis, offers insights into dataset structures and drives sophisticated analytical procedures. While unimodality's confirmation is straightforward for one-dimensional data using methods like Silverman's approach and Hartigans' dip statistic, its generalization to higher dimensions remains challenging. By extrapolating one-dimensional unimodality principles to multi-dimensional spaces through linear random projections and leveraging point-to-point distancing, our method, rooted in $\alpha$-unimodality assumptions, presents a novel multivariate unimodality test named mud-pod. Both theoretical and empirical studies confirm the efficacy of our method in unimodality assessment of multidimensional datasets as well as in estimating the number of clusters.
With the increasing popularity of conversational search, how to evaluate the performance of conversational search systems has become an important question in the IR community. Existing works on conversational search evaluation can mainly be categorized into two streams: (1) constructing metrics based on semantic similarity (e.g. BLUE, METEOR and BERTScore), or (2) directly evaluating the response ranking performance of the system using traditional search methods (e.g. nDCG, RBP and nERR). However, these methods either ignore the information need of the user or ignore the mixed-initiative property of conversational search. This raises the question of how to accurately model user satisfaction in conversational search scenarios. Since explicitly asking users to provide satisfaction feedback is difficult, traditional IR studies often rely on the Cranfield paradigm (i.e., third-party annotation) and user behavior modeling to estimate user satisfaction in search. However, the feasibility and effectiveness of these two approaches have not been fully explored in conversational search. In this paper, we dive into the evaluation of conversational search from the perspective of user satisfaction. We build a novel conversational search experimental platform and construct a Chinese open-domain conversational search behavior dataset containing rich annotations and search behavior data. We also collect third-party satisfaction annotation at the session-level and turn-level, to investigate the feasibility of the Cranfield paradigm in the conversational search scenario. Experimental results show both some consistency and considerable differences between the user satisfaction annotations and third-party annotations. We also propose dialog continuation or ending behavior models (DCEBM) to capture session-level user satisfaction based on turn-level information.
This study explores the impact of peer acknowledgement on learner engagement and implicit psychological attributes in written annotations on an online social reading platform. Participants included 91 undergraduates from a large North American University. Using log file data, we analyzed the relationship between learners' received peer acknowledgement and their subsequent annotation behaviours using cross-lag regression. Higher peer acknowledgements correlate with increased initiation of annotations and responses to peer annotations. By applying text mining techniques and calculating Shapley values to analyze 1,969 social annotation entries, we identified prominent psychological themes within three dimensions (i.e., affect, cognition, and motivation) that foster peer acknowledgment in digital social annotation. These themes include positive affect, openness to learning and discussion, and expression of motivation. The findings assist educators in improving online learning communities and provide guidance to technology developers in designing effective prompts, drawing from both implicit psychological cues and explicit learning behaviours.
Many iterative algorithms in optimization, computational geometry, computer algebra, and other areas of computer science require repeated computation of some algebraic expression whose input changes slightly from one iteration to the next. Although efficient data structures have been proposed for maintaining the solution of such algebraic expressions under low-rank updates, most of these results are only analyzed under exact arithmetic (real-RAM model and finite fields) which may not accurately reflect the complexity guarantees of real computers. In this paper, we analyze the stability and bit complexity of such data structures for expressions that involve the inversion, multiplication, addition, and subtraction of matrices under the word-RAM model. We show that the bit complexity only increases linearly in the number of matrix operations in the expression. In addition, we consider the bit complexity of maintaining the determinant of a matrix expression. We show that the required bit complexity depends on the logarithm of the condition number of matrices instead of the logarithm of their determinant. We also discuss rank maintenance and its connections to determinant maintenance. Our results have wide applications ranging from computational geometry (e.g., computing the volume of a polytope) to optimization (e.g., solving linear programs using the simplex algorithm).
To investigate causal mechanisms, causal mediation analysis decomposes the total treatment effect into the natural direct and indirect effects. This paper examines the estimation of the direct and indirect effects in a general treatment effect model, where the treatment can be binary, multi-valued, continuous, or a mixture. We propose generalized weighting estimators with weights estimated by solving an expanding set of equations. Under some sufficient conditions, we show that the proposed estimators are consistent and asymptotically normal. Specifically, when the treatment is discrete, the proposed estimators attain the semiparametric efficiency bounds. Meanwhile, when the treatment is continuous, the convergence rates of the proposed estimators are slower than $N^{-1/2}$; however, they are still more efficient than that constructed from the true weighting function. A simulation study reveals that our estimators exhibit a satisfactory finite-sample performance, while an application shows their practical value
While the body of research directed towards constructing and generating clarifying questions in mixed-initiative conversational search systems is vast, research aimed at processing and comprehending users' answers to such questions is scarce. To this end, we present a simple yet effective method for processing answers to clarifying questions, moving away from previous work that simply appends answers to the original query and thus potentially degrades retrieval performance. Specifically, we propose a classifier for assessing usefulness of the prompted clarifying question and an answer given by the user. Useful questions or answers are further appended to the conversation history and passed to a transformer-based query rewriting module. Results demonstrate significant improvements over strong non-mixed-initiative baselines. Furthermore, the proposed approach mitigates the performance drops when non useful questions and answers are utilized.
In geostatistics, block likelihood offers a balance between statistical accuracy and computational efficiency when estimating covariance functions. This balance is reached by dividing the sample into blocks and computing a weighted sum of (sub) log-likelihoods corresponding to pairs of blocks. Practitioners often choose block sizes ranging from hundreds to a few thousand observations, inherently involving matrix-based implementations. An alternative, residing at the opposite end of this methodological spectrum, treats each observation as a block, resulting in the matrix-free pairwise likelihood method. We propose an additional alternative within this broad methodological landscape, systematically constructing blocks of size two and merging pairs of blocks through conditioning. Importantly, our method strategically avoids large-sized blocks, facilitating explicit calculations that ultimately do not rely on matrix computations. Studies with both simulated and real data validate the effectiveness of our approach, on one hand demonstrating its superiority over pairwise likelihood, and on the other, challenging the intuitive notion that employing matrix-based versions universally lead to better statistical performance.
Recent empirical and theoretical studies have established the generalization capabilities of large machine learning models that are trained to (approximately or exactly) fit noisy data. In this work, we prove a surprising result that even if the ground truth itself is robust to adversarial examples, and the benignly overfitted model is benign in terms of the ``standard'' out-of-sample risk objective, this benign overfitting process can be harmful when out-of-sample data are subject to adversarial manipulation. More specifically, our main results contain two parts: (i) the min-norm estimator in overparameterized linear model always leads to adversarial vulnerability in the ``benign overfitting'' setting; (ii) we verify an asymptotic trade-off result between the standard risk and the ``adversarial'' risk of every ridge regression estimator, implying that under suitable conditions these two items cannot both be small at the same time by any single choice of the ridge regularization parameter. Furthermore, under the lazy training regime, we demonstrate parallel results on two-layer neural tangent kernel (NTK) model, which align with empirical observations in deep neural networks. Our finding provides theoretical insights into the puzzling phenomenon observed in practice, where the true target function (e.g., human) is robust against adverasrial attack, while beginly overfitted neural networks lead to models that are not robust.
Generating proofs of unsatisfiability is a valuable capability of most SAT solvers, and is an active area of research for SMT solvers. This paper introduces the first method to efficiently generate proofs of unsatisfiability specifically for an important subset of SMT: SAT Modulo Monotonic Theories (SMMT), which includes many useful finite-domain theories (e.g., bit vectors and many graph-theoretic properties) and is used in production at Amazon Web Services. Our method uses propositional definitions of the theory predicates, from which it generates compact Horn approximations of the definitions, which lead to efficient DRAT proofs, leveraging the large investment the SAT community has made in DRAT. In experiments on practical SMMT problems, our proof generation overhead is minimal (7.41% geometric mean slowdown, 28.8% worst-case), and we can generate and check proofs for many problems that were previously intractable.
This paper combines modern numerical computation with theoretical results to improve our understanding of the growth factor problem for Gaussian elimination. On the computational side we obtain lower bounds for the maximum growth for complete pivoting for $n=1:75$ and $n=100$ using the Julia JuMP optimization package. At $n=100$ we obtain a growth factor bigger than $3n$. The numerical evidence suggests that the maximum growth factor is bigger than $n$ if and only if $n \ge 11$. We also present a number of theoretical results. We show that the maximum growth factor over matrices with entries restricted to a subset of the reals is nearly equal to the maximum growth factor over all real matrices. We also show that the growth factors under floating point arithmetic and exact arithmetic are nearly identical. Finally, through numerical search, and stability and extrapolation results, we provide improved lower bounds for the maximum growth factor. Specifically, we find that the largest growth factor is bigger than $1.0045n$ for $n>10$, and the lim sup of the ratio with $n$ is greater than or equal to $3.317$. In contrast to the old conjecture that growth might never be bigger than $n$, it seems likely that the maximum growth divided by $n$ goes to infinity as $n \rightarrow \infty$.
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.