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The concept of updating a probability distribution in the light of new evidence lies at the heart of statistics and machine learning. Pearl's and Jeffrey's rule are two natural update mechanisms which lead to different outcomes, yet the similarities and differences remain mysterious. This paper clarifies their relationship in several ways: via separate descriptions of the two update mechanisms in terms of probabilistic programs and sampling semantics, and via different notions of likelihood (for Pearl and for Jeffrey). Moreover, it is shown that Jeffrey's update rule arises via variational inference. In terms of categorical probability theory, this amounts to an analysis of the situation in terms of the behaviour of the multiset functor, extended to the Kleisli category of the distribution monad.

Quality Diversity (QD) algorithms have been proposed to search for a large collection of both diverse and high-performing solutions instead of a single set of local optima. While early QD algorithms view the objective and descriptor functions as black-box functions, novel tools have been introduced to use gradient information to accelerate the search and improve overall performance of those algorithms over continuous input spaces. However a broad range of applications involve discrete spaces, such as drug discovery or image generation. Exploring those spaces is challenging as they are combinatorially large and gradients cannot be used in the same manner as in continuous spaces. We introduce map-elites with a Gradient-Informed Discrete Emitter (ME-GIDE), which extends QD optimisation with differentiable functions over discrete search spaces. ME-GIDE leverages the gradient information of the objective and descriptor functions with respect to its discrete inputs to propose gradient-informed updates that guide the search towards a diverse set of high quality solutions. We evaluate our method on challenging benchmarks including protein design and discrete latent space illumination and find that our method outperforms state-of-the-art QD algorithms in all benchmarks.

The acoustic variability of noisy and reverberant speech mixtures is influenced by multiple factors, such as the spectro-temporal characteristics of the target speaker and the interfering noise, the signal-to-noise ratio (SNR) and the room characteristics. This large variability poses a major challenge for learning-based speech enhancement systems, since a mismatch between the training and testing conditions can substantially reduce the performance of the system. Generalization to unseen conditions is typically assessed by testing the system with a new speech, noise or binaural room impulse response (BRIR) database different from the one used during training. However, the difficulty of the speech enhancement task can change across databases, which can substantially influence the results. The present study introduces a generalization assessment framework that uses a reference model trained on the test condition, such that it can be used as a proxy for the difficulty of the test condition. This allows to disentangle the effect of the change in task difficulty from the effect of dealing with new data, and thus to define a new measure of generalization performance termed the generalization gap. The procedure is repeated in a cross-validation fashion by cycling through multiple speech, noise, and BRIR databases to accurately estimate the generalization gap. The proposed framework is applied to evaluate the generalization potential of a feedforward neural network (FFNN), Conv-TasNet, DCCRN and MANNER. We find that for all models, the performance degrades the most in speech mismatches, while good noise and room generalization can be achieved by training on multiple databases. Moreover, while recent models show higher performance in matched conditions, their performance substantially decreases in mismatched conditions and can become inferior to that of the FFNN-based system.

The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular (spectral) measure and the density of the norm. The support of the angular measure is the surface of a unit hypersphere and the density of the norm corresponds to a Pareto density. The dependence structure is determined by the angular measure on the hypersphere, and directions with high probability characterize the dependence structure among the elements of the random vector of extreme values. Previous applications of the regular variation model have not considered a probabilistic model for the angular density and no statistical tests were applied. In this paper, circular and spherical distributions based on nonnegative trigonometric sums are considered flexible probabilistic models for the spectral measure that allows the application of statistical tests to make inferences about the dependence structure among extreme values. The proposed methodology is applied to real datasets from finance.

Since the introduction of DeepMimic [Peng et al. 2018], subsequent research has focused on expanding the repertoire of simulated motions across various scenarios. In this study, we propose an alternative approach for this goal, a deep reinforcement learning method based on the simulation of a single-rigid-body character. Using the centroidal dynamics model (CDM) to express the full-body character as a single rigid body (SRB) and training a policy to track a reference motion, we can obtain a policy that is capable of adapting to various unobserved environmental changes and controller transitions without requiring any additional learning. Due to the reduced dimension of state and action space, the learning process is sample-efficient. The final full-body motion is kinematically generated in a physically plausible way, based on the state of the simulated SRB character. The SRB simulation is formulated as a quadratic programming (QP) problem, and the policy outputs an action that allows the SRB character to follow the reference motion. We demonstrate that our policy, efficiently trained within 30 minutes on an ultraportable laptop, has the ability to cope with environments that have not been experienced during learning, such as running on uneven terrain or pushing a box, and transitions between learned policies, without any additional learning.

The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic codes and almost quasi-cyclic codes are discussed in detail, presenting necessary and sufficient conditions for which linear codes with such an automorphism are self-orthogonal, self-dual, or linear complementary dual.

Molecule discovery serves as a cornerstone in numerous scientific domains, fueling the development of new materials and innovative drug designs. Recent developments of in-silico molecule discovery have highlighted the promising results of cross-modal techniques, which bridge molecular structures with their descriptive annotations. However, these cross-modal methods frequently encounter the issue of data scarcity, hampering their performance and application. In this paper, we address the low-resource challenge by utilizing artificially-real data generated by Large Language Models (LLMs). We first introduce a retrieval-based prompting strategy to construct high-quality pseudo data, then explore the optimal method to effectively leverage this pseudo data. Experiments show that using pseudo data for domain adaptation outperforms all existing methods, while also requiring a smaller model scale, reduced data size and lower training cost, highlighting its efficiency. Furthermore, our method shows a sustained improvement as the volume of pseudo data increases, revealing the great potential of pseudo data in advancing low-resource cross-modal molecule discovery.

Benkeser et al. demonstrate how adjustment for baseline covariates in randomized trials can meaningfully improve precision for a variety of outcome types. Their findings build on a long history, starting in 1932 with R.A. Fisher and including more recent endorsements by the U.S. Food and Drug Administration and the European Medicines Agency. Here, we address an important practical consideration: *how* to select the adjustment approach -- which variables and in which form -- to maximize precision, while maintaining Type-I error control. Balzer et al. previously proposed *Adaptive Prespecification* within TMLE to flexibly and automatically select, from a prespecified set, the approach that maximizes empirical efficiency in small trials (N$<$40). To avoid overfitting with few randomized units, selection was previously limited to working generalized linear models, adjusting for a single covariate. Now, we tailor Adaptive Prespecification to trials with many randomized units. Using $V$-fold cross-validation and the estimated influence curve-squared as the loss function, we select from an expanded set of candidates, including modern machine learning methods adjusting for multiple covariates. As assessed in simulations exploring a variety of data generating processes, our approach maintains Type-I error control (under the null) and offers substantial gains in precision -- equivalent to 20-43\% reductions in sample size for the same statistical power. When applied to real data from ACTG Study 175, we also see meaningful efficiency improvements overall and within subgroups.

The circular uniform distribution on the unit circle is closed under summation, that is, the sum of independent circular uniformly distributed random variables is also circular uniformly distributed. In this study, it is shown that a family of circular distributions based on nonnegative trigonometric sums (NNTS) is also closed under summation. Given the flexibility of NNTS circular distributions to model multimodality and skewness, these are good candidates for use as alternative models to test for circular uniformity to detect different deviations from the null hypothesis of circular uniformity. The circular uniform distribution is a member of the NNTS family, but in the NNTS parameter space, it corresponds to a point on the boundary of the parameter space, implying that the regularity conditions are not satisfied when the parameters are estimated by using the maximum likelihood method. Two NNTS tests for circular uniformity were developed by considering the standardised maximum likelihood estimator and the generalised likelihood ratio. Given the nonregularity condition, the critical values of the proposed NNTS circular uniformity tests were obtained via simulation and interpolated for any sample size by the fitting of regression models. The validity of the proposed NNTS circular uniformity tests was evaluated by generating NNTS models close to the circular uniformity null hypothesis.

We study how to mitigate the effects of energy attacks in the batteryless Internet of Things (IoT). Battery-less IoT devices live and die with ambient energy, as they use energy harvesting to power their operation. They are employed in a multitude of applications, including safety-critical ones such as biomedical implants. Due to scarce energy intakes and limited energy buffers, their executions become intermittent, alternating periods of active operation with periods of recharging their energy buffers. Experimental evidence exists that shows how controlling ambient energy allows an attacker to steer a device execution in unintended ways: energy provisioning effectively becomes an attack vector. We design, implement, and evaluate a mitigation system for energy attacks. By taking into account the specific application requirements and the output of an attack detection module, we tune task execution rates and optimize energy management. This ensures continued application execution in the event of an energy attack. When a device is under attack, our solution ensures the execution of 23.3% additional application cycles compared to the baselines we consider and increases task schedulability by at least 21%, while enabling a 34% higher peripheral availability.