In a sequential regression setting, a decision-maker may be primarily concerned with whether the future observation will increase or decrease compared to the current one, rather than the actual value of the future observation. In this context, we introduce the notion of parity calibration, which captures the goal of calibrated forecasting for the increase-decrease (or "parity") event in a timeseries. Parity probabilities can be extracted from a forecasted distribution for the output, but we show that such a strategy leads to theoretical unpredictability and poor practical performance. We then observe that although the original task was regression, parity calibration can be expressed as binary calibration. Drawing on this connection, we use an online binary calibration method to achieve parity calibration. We demonstrate the effectiveness of our approach on real-world case studies in epidemiology, weather forecasting, and model-based control in nuclear fusion.
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Retrieval approaches that score documents based on learned dense vectors (i.e., dense retrieval) rather than lexical signals (i.e., conventional retrieval) are increasingly popular. Their ability to identify related documents that do not necessarily contain the same terms as those appearing in the user's query (thereby improving recall) is one of their key advantages. However, to actually achieve these gains, dense retrieval approaches typically require an exhaustive search over the document collection, making them considerably more expensive at query-time than conventional lexical approaches. Several techniques aim to reduce this computational overhead by approximating the results of a full dense retriever. Although these approaches reasonably approximate the top results, they suffer in terms of recall -- one of the key advantages of dense retrieval. We introduce 'LADR' (Lexically-Accelerated Dense Retrieval), a simple-yet-effective approach that improves the efficiency of existing dense retrieval models without compromising on retrieval effectiveness. LADR uses lexical retrieval techniques to seed a dense retrieval exploration that uses a document proximity graph. We explore two variants of LADR: a proactive approach that expands the search space to the neighbors of all seed documents, and an adaptive approach that selectively searches the documents with the highest estimated relevance in an iterative fashion. Through extensive experiments across a variety of dense retrieval models, we find that LADR establishes a new dense retrieval effectiveness-efficiency Pareto frontier among approximate k nearest neighbor techniques. Further, we find that when tuned to take around 8ms per query in retrieval latency on our hardware, LADR consistently achieves both precision and recall that are on par with an exhaustive search on standard benchmarks.
Multi-modality fusion and multi-task learning are becoming trendy in 3D autonomous driving scenario, considering robust prediction and computation budget. However, naively extending the existing framework to the domain of multi-modality multi-task learning remains ineffective and even poisonous due to the notorious modality bias and task conflict. Previous works manually coordinate the learning framework with empirical knowledge, which may lead to sub-optima. To mitigate the issue, we propose a novel yet simple multi-level gradient calibration learning framework across tasks and modalities during optimization. Specifically, the gradients, produced by the task heads and used to update the shared backbone, will be calibrated at the backbone's last layer to alleviate the task conflict. Before the calibrated gradients are further propagated to the modality branches of the backbone, their magnitudes will be calibrated again to the same level, ensuring the downstream tasks pay balanced attention to different modalities. Experiments on large-scale benchmark nuScenes demonstrate the effectiveness of the proposed method, eg, an absolute 14.4% mIoU improvement on map segmentation and 1.4% mAP improvement on 3D detection, advancing the application of 3D autonomous driving in the domain of multi-modality fusion and multi-task learning. We also discuss the links between modalities and tasks.
Rare and Weak models for multiple hypothesis testing assume that only a small proportion of the tested hypotheses concern non-null effects and the individual effects are only moderately large, so they generally do not stand out individually, for example in a Bonferroni analysis. Such models have been studied in quite a few settings, for example in some cases studies focused on an underlying Gaussian means model for the hypotheses being tested; in some others, Poisson and Binomial. Such seemingly different models have asymptotically the following common structure. Summarizing the evidence of individual tests by the negative logarithm of its P-value, the model is asymptotically equivalent to a situation in which most negative log P-values have a standard exponential distribution but a small fraction of the P-values might have an alternative distribution which is approximately noncentral chisquared on one degree of freedom. This log-chisquared approximation is different from the log-normal approximation of Bahadur which is unsuitable for analyzing Rare and Weak multiple testing models. We characterize the asymptotic performance of global tests combining asymptotic log-chisquared P-values in terms of the chisquared mixture parameters: the scaling parameter controlling heteroscedasticity, the non-centrality parameter describing the effect size whenever it exists, and the parameter controlling the rarity of the non-null effects. In a phase space involving the last two parameters, we derive a region where all tests are asymptotically powerless. Outside of this region, the Berk-Jones and the Higher Criticism tests have maximal power. Inference techniques based on the minimal P-value, false-discovery rate controlling, and Fisher's combination test have sub-optimal asymptotic phase diagrams.
Modern robotic systems are required to operate in challenging environments, which demand reliable localization under challenging conditions. LiDAR-based localization methods, such as the Iterative Closest Point (ICP) algorithm, can suffer in geometrically uninformative environments that are known to deteriorate point cloud registration performance and push optimization toward divergence along weakly constrained directions. To overcome this issue, this work proposes i) a robust fine-grained localizability detection module, and ii) a localizability-aware constrained ICP optimization module, which couples with the localizability detection module in a unified manner. The proposed localizability detection is achieved by utilizing the correspondences between the scan and the map to analyze the alignment strength against the principal directions of the optimization as part of its fine-grained LiDAR localizability analysis. In the second part, this localizability analysis is then integrated into the scan-to-map point cloud registration to generate drift-free pose updates by enforcing controlled updates or leaving the degenerate directions of the optimization unchanged. The proposed method is thoroughly evaluated and compared to state-of-the-art methods in simulated and real-world experiments, demonstrating the performance and reliability improvement in LiDAR-challenging environments. In all experiments, the proposed framework demonstrates accurate and generalizable localizability detection and robust pose estimation without environment-specific parameter tuning.
Hand-eye calibration is the problem of estimating the spatial transformation between a reference frame, usually the base of a robot arm or its gripper, and the reference frame of one or multiple cameras. Generally, this calibration is solved as a non-linear optimization problem, what instead is rarely done is to exploit the underlying graph structure of the problem itself. Actually, the problem of hand-eye calibration can be seen as an instance of the Simultaneous Localization and Mapping (SLAM) problem. Inspired by this fact, in this work we present a pose-graph approach to the hand-eye calibration problem that extends a recent state-of-the-art solution in two different ways: i) by formulating the solution to eye-on-base setups with one camera; ii) by covering multi-camera robotic setups. The proposed approach has been validated in simulation against standard hand-eye calibration methods. Moreover, a real application is shown. In both scenarios, the proposed approach overcomes all alternative methods. We release with this paper an open-source implementation of our graph-based optimization framework for multi-camera setups.
In a well-calibrated risk prediction model, the average predicted probability is close to the true event rate for any given subgroup. Such models are reliable across heterogeneous populations and satisfy strong notions of algorithmic fairness. However, the task of auditing a model for strong calibration is well-known to be difficult -- particularly for machine learning (ML) algorithms -- due to the sheer number of potential subgroups. As such, common practice is to only assess calibration with respect to a few predefined subgroups. Recent developments in goodness-of-fit testing offer potential solutions but are not designed for settings with weak signal or where the poorly calibrated subgroup is small, as they either overly subdivide the data or fail to divide the data at all. We introduce a new testing procedure based on the following insight: if we can reorder observations by their expected residuals, there should be a change in the association between the predicted and observed residuals along this sequence if a poorly calibrated subgroup exists. This lets us reframe the problem of calibration testing into one of changepoint detection, for which powerful methods already exist. We begin with introducing a sample-splitting procedure where a portion of the data is used to train a suite of candidate models for predicting the residual, and the remaining data are used to perform a score-based cumulative sum (CUSUM) test. To further improve power, we then extend this adaptive CUSUM test to incorporate cross-validation, while maintaining Type I error control under minimal assumptions. Compared to existing methods, the proposed procedure consistently achieved higher power in simulation studies and more than doubled the power when auditing a mortality risk prediction model.
The processing of information is an indispensable property of living systems realized by networks of active processes with enormous complexity. They have inspired many variants of modern machine learning one of them being reservoir computing, in which stimulating a network of nodes with fading memory enables computations and complex predictions. Reservoirs are implemented on computer hardware, but also on unconventional physical substrates such as mechanical oscillators, spins, or bacteria often summarized as physical reservoir computing. Here we demonstrate physical reservoir computing with a synthetic active microparticle system that self-organizes from an active and passive component into inherently noisy nonlinear dynamical units. The self-organization and dynamical response of the unit is the result of a delayed propulsion of the microswimmer to a passive target. A reservoir of such units with a self-coupling via the delayed response can perform predictive tasks despite the strong noise resulting from Brownian motion of the microswimmers. To achieve efficient noise suppression, we introduce a special architecture that uses historical reservoir states for output. Our results pave the way for the study of information processing in synthetic self-organized active particle systems.
Coded distributed computing, proposed by Li et al., offers significant potential for reducing the communication load in MapReduce computing systems. In the setting of the \emph{cascaded} coded distributed computing that consisting of $K$ nodes, $N$ input files, and $Q$ output functions, the objective is to compute each output function through $s\geq 1$ nodes with a computation load $r\geq 1$, enabling the application of coding techniques during the Shuffle phase to achieve minimum communication load. However, for most existing coded distributed computing schemes, a major limitation lies in their demand for splitting the original data into an exponentially growing number of input files in terms of $N/\binom{K}{r} \in\mathbb{N}$ and requiring an exponentially large number of output functions $Q/\binom{K}{s} \in\mathbb{N}$, which imposes stringent requirements for implementation and results in significant coding complexity when $K$ is large. In this paper, we focus on the cascaded case of $K/s\in\mathbb{N} $, deliberately designing the strategy of input files store and output functions assignment based on a grouping method, such that a low-complexity two-round Shuffle phase is available. The main advantages of our proposed scheme contains: 1) the communication load is quilt close to or surprisingly better than the optimal state-of-the-art scheme proposed by Li et al.; 2) our scheme requires significantly less number of input files and output functions; 3) all the operations are implemented over the minimum binary field $\mathbb{F}_2$.
Complex interactions between two opposing agents frequently occur in domains of machine learning, game theory, and other application domains. Quantitatively analyzing the strategies involved can provide an objective basis for decision-making. One such critical scenario is shot-taking in football, where decisions, such as whether the attacker should shoot or pass the ball and whether the defender should attempt to block the shot, play a crucial role in the outcome of the game. However, there are currently no effective data-driven and/or theory-based approaches to analyzing such situations. To address this issue, we proposed a novel framework to analyze such scenarios based on game theory, where we estimate the expected payoff with machine learning (ML) models, and additional features for ML models were extracted with a theory-based shot block model. Conventionally, successes or failures (1 or 0) are used as payoffs, while a success shot (goal) is extremely rare in football. Therefore, we proposed the Expected Probability of Shot On Target (xSOT) metric to evaluate players' actions even if the shot results in no goal; this allows for effective differentiation and comparison between different shots and even enables counterfactual shot situation analysis. In our experiments, we have validated the framework by comparing it with baseline and ablated models. Furthermore, we have observed a high correlation between the xSOT and existing metrics. This alignment of information suggests that xSOT provides valuable insights. Lastly, as an illustration, we studied optimal strategies in the World Cup 2022 and analyzed a shot situation in EURO 2020.
Ranking functions that are used in decision systems often produce disparate results for different populations because of bias in the underlying data. Addressing, and compensating for, these disparate outcomes is a critical problem for fair decision-making. Recent compensatory measures have mostly focused on opaque transformations of the ranking functions to satisfy fairness guarantees or on the use of quotas or set-asides to guarantee a minimum number of positive outcomes to members of underrepresented groups. In this paper we propose easily explainable data-driven compensatory measures for ranking functions. Our measures rely on the generation of bonus points given to members of underrepresented groups to address disparity in the ranking function. The bonus points can be set in advance, and can be combined, allowing for considering the intersections of representations and giving better transparency to stakeholders. We propose efficient sampling-based algorithms to calculate the number of bonus points to minimize disparity. We validate our algorithms using real-world school admissions and recidivism datasets, and compare our results with that of existing fair ranking algorithms.
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