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In pseudo-labeling (PL), which is a type of semi-supervised learning, pseudo-labels are assigned based on the confidence scores provided by the classifier; therefore, accurate confidence is important for successful PL. In this study, we propose a PL algorithm based on an energy-based model (EBM), which is referred to as the energy-based PL (EBPL). In EBPL, a neural network-based classifier and an EBM are jointly trained by sharing their feature extraction parts. This approach enables the model to learn both the class decision boundary and input data distribution, enhancing confidence calibration during network training. The experimental results demonstrate that EBPL outperforms the existing PL method in semi-supervised image classification tasks, with superior confidence calibration error and recognition accuracy.

This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on recasting the optimisation of scoring rules as an assignment problem, which is solved using quadratic programming. The proposed framework produces coherent joint probabilistic forecasts for count hierarchical time series. Two discrete reconciliation algorithms are also proposed and compared against generalisations of the top-down and bottom-up approaches for count data. Two simulation experiments and two empirical examples are conducted to validate that the proposed reconciliation algorithms improve forecast accuracy. The empirical applications are forecasting criminal offences in Washington D.C. and product unit sales in the M5 dataset. Compared to benchmarks, the proposed framework shows superior performance in both simulations and empirical studies.

Analyses of voting algorithms often overlook informational externalities shaping individual votes. For example, pre-polling information often skews voters towards candidates who may not be their top choice, but who they believe would be a worthwhile recipient of their vote. In this work, we aim to understand the role of external information in voting outcomes. We study this by analyzing (1) the probability that voting outcomes align with external information, and (2) the effect of external information on the total utility across voters, or social welfare. In practice, voting mechanisms elicit coarse information about voter utilities, such as ordinal preferences, which initially prevents us from directly analyzing the effect of informational externalities with standard voting mechanisms. To overcome this, we present an intermediary mechanism for learning how preferences change with external information which does not require eliciting full cardinal preferences. With this tool in hand, we find that voting mechanisms are generally more likely to select the alternative most favored by the external information, and when external information reflects the population's true preferences, social welfare increases in expectation.

The Conformer has become the most popular encoder model for automatic speech recognition (ASR). It adds convolution modules to a transformer to learn both local and global dependencies. In this work we describe a faster, more memory-efficient, and better-performing transformer, called Zipformer. Modeling changes include: 1) a U-Net-like encoder structure where middle stacks operate at lower frame rates; 2) reorganized block structure with more modules, within which we re-use attention weights for efficiency; 3) a modified form of LayerNorm called BiasNorm allows us to retain some length information; 4) new activation functions SwooshR and SwooshL work better than Swish. We also propose a new optimizer, called ScaledAdam, which scales the update by each tensor's current scale to keep the relative change about the same, and also explictly learns the parameter scale. It achieves faster convergence and better performance than Adam. Extensive experiments on LibriSpeech, Aishell-1, and WenetSpeech datasets demonstrate the effectiveness of our proposed Zipformer over other state-of-the-art ASR models. Our code is publicly available at //github.com/k2-fsa/icefall.

Every equi-isoclinic tight fusion frame (EITFF) is a type of optimal code in a Grassmannian, consisting of subspaces of a finite-dimensional Hilbert space for which the smallest principal angle between any pair of them is as large as possible. EITFFs yield dictionaries with minimal block coherence and so are ideal for certain types of compressed sensing. By refining classical arguments of Lemmens and Seidel that rely upon Radon-Hurwitz theory, we fully characterize EITFFs in the special case where the dimension of the subspaces is exactly one-half of that of the ambient space. We moreover show that each such "Radon-Hurwitz EITFF" is highly symmetric.

We exploit the similarities between Tikhonov regularization and Bayesian hierarchical models to propose a regularization scheme that acts like a distributed Tikhonov regularization where the amount of regularization varies from component to component. In the standard formulation, Tikhonov regularization compensates for the inherent ill-conditioning of linear inverse problems by augmenting the data fidelity term measuring the mismatch between the data and the model output with a scaled penalty functional. The selection of the scaling is the core problem in Tikhonov regularization. If an estimate of the amount of noise in the data is available, a popular way is to use the Morozov discrepancy principle, stating that the scaling parameter should be chosen so as to guarantee that the norm of the data fitting error is approximately equal to the norm of the noise in the data. A too small value of the regularization parameter would yield a solution that fits to the noise while a too large value would lead to an excessive penalization of the solution. In many applications, it would be preferable to apply distributed regularization, replacing the regularization scalar by a vector valued parameter, allowing different regularization for different components of the unknown, or for groups of them. A distributed Tikhonov-inspired regularization is particularly well suited when the data have significantly different sensitivity to different components, or to promote sparsity of the solution. The numerical scheme that we propose, while exploiting the Bayesian interpretation of the inverse problem and identifying the Tikhonov regularization with the Maximum A Posteriori (MAP) estimation, requires no statistical tools. A combination of numerical linear algebra and optimization tools makes the scheme computationally efficient and suitable for problems where the matrix is not explicitly available.

Threshold selection is a fundamental problem in any threshold-based extreme value analysis. While models are asymptotically motivated, selecting an appropriate threshold for finite samples is difficult and highly subjective through standard methods. Inference for high quantiles can also be highly sensitive to the choice of threshold. Too low a threshold choice leads to bias in the fit of the extreme value model, while too high a choice leads to unnecessary additional uncertainty in the estimation of model parameters. We develop a novel methodology for automated threshold selection that directly tackles this bias-variance trade-off. We also develop a method to account for the uncertainty in the threshold estimation and propagate this uncertainty through to high quantile inference. Through a simulation study, we demonstrate the effectiveness of our method for threshold selection and subsequent extreme quantile estimation, relative to the leading existing methods, and show how the method's effectiveness is not sensitive to the tuning parameters. We apply our method to the well-known, troublesome example of the River Nidd dataset.

State-of-the-art LiDAR calibration frameworks mainly use non-probabilistic registration methods such as Iterative Closest Point (ICP) and its variants. These methods suffer from biased results due to their pair-wise registration procedure as well as their sensitivity to initialization and parameterization. This often leads to misalignments in the calibration process. Probabilistic registration methods compensate for these drawbacks by specifically modeling the probabilistic nature of the observations. This paper presents GMMCalib, an automatic target-based extrinsic calibration approach for multi-LiDAR systems. Using an implementation of a Gaussian Mixture Model (GMM)-based registration method that allows joint registration of multiple point clouds, this data-driven approach is compared to ICP algorithms. We perform simulation experiments using the digital twin of the EDGAR research vehicle and validate the results in a real-world environment. We also address the local minima problem of local registration methods for extrinsic sensor calibration and use a distance-based metric to evaluate the calibration results. Our results show that an increase in robustness against sensor miscalibrations can be achieved by using GMM-based registration algorithms. The code is open source and available on GitHub.

In-context learning can improve the performances of knowledge-rich tasks such as question answering. In such scenarios, in-context examples trigger a language model (LM) to surface information stored in its parametric knowledge. We study how to better construct in-context example sets, based on whether the model is aware of the in-context examples. We identify 'known' examples, where models can correctly answer from their parametric knowledge, and 'unknown' ones. Our experiments show that prompting with 'unknown' examples decreases the performance, potentially as it encourages hallucination rather than searching for its parametric knowledge. Constructing an in-context example set that presents both known and unknown information performs the best across diverse settings. We perform analysis on three multi-answer question answering datasets, which allows us to further study answer set ordering strategies based on the LM's knowledge of each answer. Together, our study sheds light on how to best construct in-context example sets for knowledge-rich tasks.

In this paper, we introduce the cumulative past information generating function (CPIG) and relative cumulative past information generating function (RCPIG). We study its properties. We establish its relation with generalized cumulative past entropy (GCPE). We defined CPIG stochastic order and its relation with dispersive order. We provide the results for the CPIG measure of the convoluted random variables in terms of the measures of its components. We found some inequality relating to Shannon entropy, CPIG and GCPE. Some characterization and estimation results are also discussed regarding CPIG. We defined divergence measures between two random variables, Jensen-cumulative past information generating function(JCPIG), Jensen fractional cumulative past entropy measure, cumulative past Taneja entropy, and Jensen cumulative past Taneja entropy information measure.