Understanding the structure, quantity, and type of snow in mountain landscapes is crucial for assessing avalanche safety, interpreting satellite imagery, building accurate hydrology models, and choosing the right pair of skis for your weekend trip. Currently, such characteristics of snowpack are measured using a combination of remote satellite imagery, weather stations, and laborious point measurements and descriptions provided by local forecasters, guides, and backcountry users. Here, we explore how characteristics of the top layer of snowpack could be estimated while skiing using strain sensors mounted to the top surface of an alpine ski. We show that with two strain gauges and an inertial measurement unit it is feasible to correctly assign one of three qualitative labels (powder, slushy, or icy/groomed snow) to each 10 second segment of a trajectory with 97% accuracy, independent of skiing style. Our algorithm uses a combination of a data-driven linear model of the ski-snow interaction, dimensionality reduction, and a Naive Bayes classifier. Comparisons of classifier performance between strain gauges suggest that the optimal placement of strain gauges is halfway between the binding and the tip/tail of the ski, in the cambered section just before the point where the unweighted ski would touch the snow surface. The ability to classify snow, potentially in real-time, using skis opens the door to applications that range from citizen science efforts to map snow surface characteristics in the backcountry, and develop skis with automated stiffness tuning based on the snow type.

There has been an encouraging progress in the affective states recognition models based on the single-modality signals as electroencephalogram (EEG) signals or peripheral physiological signals in recent years. However, multimodal physiological signals-based affective states recognition methods have not been thoroughly exploited yet. Here we propose Multiscale Convolutional Neural Networks (Multiscale CNNs) and a biologically inspired decision fusion model for multimodal affective states recognition. Firstly, the raw signals are pre-processed with baseline signals. Then, the High Scale CNN and Low Scale CNN in Multiscale CNNs are utilized to predict the probability of affective states output for EEG and each peripheral physiological signal respectively. Finally, the fusion model calculates the reliability of each single-modality signals by the Euclidean distance between various class labels and the classification probability from Multiscale CNNs, and the decision is made by the more reliable modality information while other modalities information is retained. We use this model to classify four affective states from the arousal valence plane in the DEAP and AMIGOS dataset. The results show that the fusion model improves the accuracy of affective states recognition significantly compared with the result on single-modality signals, and the recognition accuracy of the fusion result achieve 98.52% and 99.89% in the DEAP and AMIGOS dataset respectively.

Latent Class Models (LCMs) are used to cluster multivariate categorical data (e.g. group participants based on survey responses). Traditional LCMs assume a property called conditional independence. This assumption can be restrictive, leading to model misspecification and overparameterization. To combat this problem, we developed a novel Bayesian model called a Dependent Latent Class Model (DLCM), which permits conditional dependence. We verify identifiability of DLCMs. We also demonstrate the effectiveness of DLCMs in both simulations and real-world applications. Compared to traditional LCMs, DLCMs are effective in applications with time series, overlapping items, and structural zeroes.

Causal datasets play a critical role in advancing the field of causality. However, existing datasets often lack the complexity of real-world issues such as selection bias, unfaithful data, and confounding. To address this gap, we propose a new synthetic causal dataset, the Structurally Complex with Additive paRent causalitY (SCARY) dataset, which includes the following features. The dataset comprises 40 scenarios, each generated with three different seeds, allowing researchers to leverage relevant subsets of the dataset. Additionally, we use two different data generation mechanisms for generating the causal relationship between parents and child nodes, including linear and mixed causal mechanisms with multiple sub-types. Our dataset generator is inspired by the Causal Discovery Toolbox and generates only additive models. The dataset has a Varsortability (Reisach et al., 2021) of 0.5. Our SCARY dataset provides a valuable resource for researchers to explore causal discovery under more realistic scenarios. The dataset is available at https://github.com/JayJayc/SCARY.

We present a computationally-efficient strategy to initialise the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Our strategy can be used as a pretraining stage to find initial conditions for maximum-likelihood (ML) training, or as a standalone method to compute hyperparameters values to be plugged in directly into the GP model. Motivated by the fact that training a GP via ML is equivalent (on average) to minimising the KL-divergence between the true and learnt model, we set to explore different metrics/divergences among GPs that are computationally inexpensive and provide hyperparameter values that are close to those found via ML. In practice, we identify the GP hyperparameters by projecting the empirical covariance or (Fourier) power spectrum onto a parametric family, thus proposing and studying various measures of discrepancy operating on the temporal and frequency domains. Our contribution extends the variogram method developed by the geostatistics literature and, accordingly, it is referred to as the generalised variogram method (GVM). In addition to the theoretical presentation of GVM, we provide experimental validation in terms of accuracy, consistency with ML and computational complexity for different kernels using synthetic and real-world data.

Demand for battery systems is increasing rapidly as efforts Prognosis (i.e., future prediction) in this framework is to decarbonise electricity grids and electrify mobility gather achieved using a separate model for the evolution of parameters pace [1]. Due to their long lifetime and high energy density, over battery lifetime, and this can range from a random Li-ion cells have become the workhorse in battery systems walk [8]-[10] to semi-empirical curve fits of trajectories that [2]. Although the cost of these has dramatically decreased in may be re-parameterised over lifetime using adaptive methods the last decade [3], the economics of storage needs to further such as particle filtering [13], [14], a Bayesian approach improve to increase take-up, notably in applications where that also provides parameter uncertainty estimates. Modeldriven battery systems are not yet competitive in terms of levelized approaches tend to use rather simple equivalent-circuit cost [4]. Also, given the risks of Li-ion cell demand outpacing models because they have relatively few parameters that need the supply of the required raw materials [5], it is crucial that to be fitted, whereas parameterising physics-based models, the performance of existing systems, especially in terms of such as those within the Doyle-Fuller-Newman framework lifetime, is maximised. A key element in improving the overall [15], [16], is plagued by poor identifiability [17]. This is cost-effectiveness of Li-ion batteries is accurate estimation mainly due to a lack of reference electrodes in commercial and prediction of battery state-of-health (SOH), which can cells which means that decoupling the positive and negative improve lifetime, warranty and insurance costs, system safety half-cell potentials is very difficult.

Association rule mining (ARM) was first introduced by Agrawal [1] to solve the grocery basket problem, and since then it has found numerous applications in Knowledge Discovery in Database (KDD) problems ranging from financial analysis [2] to medical diagnostics [3]. An association rule (AR) is an implication of the form A C, which can be read as "if antecedent A is true then consequent C must be true", where A and C are sets of different items (itemsets) in a database. An AR is defined by its antecedent, its consequent and two measures [4].The first one is the support, which is the proportion of rows in the dataset where both the antecedent and the consequent appear. The second measure is the confidence, the conditional probability to observe the consequent given an observation of the antecedent. The most widely-used mining strategies Apriori [1] and other exhaustive strategies [5, 6, 7] typically work by first mining frequent itemsets, then combining those itemsets to produce association rules. However, all these algorithms face the same problems: the number of rules they produce increases exponentially with the number of items in the database, and thus it becomes impossible for a human to sort through the rules returned to pick out the best ones [8]. Their execution time also become an issue with massive datasets [8]. Finally, these algorithms need support and confidence thresholds in order to efficiently search through the solution space, and those thresholds need to be carefully chosen: low values can lead to long execution times and an overabundance of rules, while high values cause the algorithm to miss interesting rules.

Large language models (LLMs) are known for their exceptional performance in natural language processing, making them highly effective in many human life-related or even job-related tasks. The attention mechanism in the Transformer architecture is a critical component of LLMs, as it allows the model to selectively focus on specific input parts. The softmax unit, which is a key part of the attention mechanism, normalizes the attention scores. Hence, the performance of LLMs in various NLP tasks depends significantly on the crucial role played by the attention mechanism with the softmax unit. In-context learning, as one of the celebrated abilities of recent LLMs, is an important concept in querying LLMs such as ChatGPT. Without further parameter updates, Transformers can learn to predict based on few in-context examples. However, the reason why Transformers becomes in-context learners is not well understood. Recently, several works [ASA+22,GTLV22,ONR+22] have studied the in-context learning from a mathematical perspective based on a linear regression formulation $\min_x\| Ax - b \|_2$, which show Transformers' capability of learning linear functions in context. In this work, we study the in-context learning based on a softmax regression formulation $\min_{x} \| \langle \exp(Ax), {\bf 1}_n \rangle^{-1} \exp(Ax) - b \|_2$ of Transformer's attention mechanism. We show the upper bounds of the data transformations induced by a single self-attention layer and by gradient-descent on a $\ell_2$ regression loss for softmax prediction function, which imply that when training self-attention-only Transformers for fundamental regression tasks, the models learned by gradient-descent and Transformers show great similarity.

Many games feature a progression of levels that doesn't adapt to the player. This can be problematic because some players may get stuck if the progression is too difficult, while others may find it boring if the progression is too slow to get to more challenging levels. This can be addressed by building levels based on the player's performance and preferences. In this work, we formulate the problem of generating levels for a player as a Markov Decision Process (MDP) and use adaptive dynamic programming (ADP) to solve the MDP before assembling a level. We tested with two case studies and found that using an ADP outperforms two baselines. Furthermore, we experimented with player proxies and switched them in the middle of play, and we show that a simple modification prior to running ADP results in quick adaptation. By using ADP, which searches the entire MDP, we produce a dynamic progression of levels that adapts to the player.

We investigate whether Deep Reinforcement Learning (Deep RL) is able to synthesize sophisticated and safe movement skills for a low-cost, miniature humanoid robot that can be composed into complex behavioral strategies in dynamic environments. We used Deep RL to train a humanoid robot with 20 actuated joints to play a simplified one-versus-one (1v1) soccer game. We first trained individual skills in isolation and then composed those skills end-to-end in a self-play setting. The resulting policy exhibits robust and dynamic movement skills such as rapid fall recovery, walking, turning, kicking and more; and transitions between them in a smooth, stable, and efficient manner - well beyond what is intuitively expected from the robot. The agents also developed a basic strategic understanding of the game, and learned, for instance, to anticipate ball movements and to block opponent shots. The full range of behaviors emerged from a small set of simple rewards. Our agents were trained in simulation and transferred to real robots zero-shot. We found that a combination of sufficiently high-frequency control, targeted dynamics randomization, and perturbations during training in simulation enabled good-quality transfer, despite significant unmodeled effects and variations across robot instances. Although the robots are inherently fragile, minor hardware modifications together with basic regularization of the behavior during training led the robots to learn safe and effective movements while still performing in a dynamic and agile way. Indeed, even though the agents were optimized for scoring, in experiments they walked 156% faster, took 63% less time to get up, and kicked 24% faster than a scripted baseline, while efficiently combining the skills to achieve the longer term objectives. Examples of the emergent behaviors and full 1v1 matches are available on the supplementary website.