Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient representations for such tasks, while preserving structural task-relations. In this paper, a new MTL method is proposed by leveraging low-rank tensor analysis and constructing tensorized Least Squares Support Vector Machines, namely the tLSSVM-MTL, where multilinear modelling and its nonlinear extensions can be flexibly exerted. We employ a high-order tensor for all the weights with each mode relating to an index and factorize it with CP decomposition, assigning a shared factor for all tasks and retaining task-specific latent factors along each index. Then an alternating algorithm is derived for the nonconvex optimization, where each resulting subproblem is solved by a linear system. Experimental results demonstrate promising performances of our tLSSVM-MTL.

Synthesizing realistic co-speech gestures is an important and yet unsolved problem for creating believable motions that can drive a humanoid robot to interact and communicate with human users. Such capability will improve the impressions of the robots by human users and will find applications in education, training, and medical services. One challenge in learning the co-speech gesture model is that there may be multiple viable gesture motions for the same speech utterance. The deterministic regression methods can not resolve the conflicting samples and may produce over-smoothed or damped motions. We proposed a two-stage model to address this uncertainty issue in gesture synthesis by modeling the gesture segments as discrete latent codes. Our method utilizes RQ-VAE in the first stage to learn a discrete codebook consisting of gesture tokens from training data. In the second stage, a two-level autoregressive transformer model is used to learn the prior distribution of residual codes conditioned on input speech context. Since the inference is formulated as token sampling, multiple gesture sequences could be generated given the same speech input using top-k sampling. The quantitative results and the user study showed the proposed method outperforms the previous methods and is able to generate realistic and diverse gesture motions.

The article considers semi-supervised multitask learning on a Gaussian mixture model (GMM). Using methods from statistical physics, we compute the asymptotic Bayes risk of each task in the regime of large datasets in high dimension, from which we analyze the role of task similarity in learning and evaluate the performance gain when tasks are learned together rather than separately. In the supervised case, we derive a simple algorithm that attains the Bayes optimal performance.

This work has been submitted to the IEEE for possible publication in the IEEE Transaction on Pattern Analysis and Machine Intelligence (T-PAMI) on 7 January 2022. Abstract--The artificial intelligence (AI) system designer for thermal comfort faces insufficient data recorded from the current user or overfitting due to unreliable training data. This work introduces the reliable data set for training the AI subsystem for thermal comfort. This paper presents the control algorithm based on shallow supervised learning, which is simple enough to be implemented in the Internet of Things (IoT) system for residential usage using ASHRAE RP-884 and ASHRAE Global Thermal Comfort Database II. No training data for thermal comfort is available as reliable as this dataset, but the direct use of this data can lead to overfitting. This work offers the algorithm for data filtering and semantic data augmentation for the ASHRAE database for the supervised learning process. Overfitting always becomes a problem due to the psychological aspect involved in the thermal comfort decision. The method to check the AI system based on the psychrometric chart against overfitting is presented. This paper also assesses the most important parameters needed to achieve human thermal comfort. This method can support the development of reinforced learning for thermal comfort. HE decarbonising heat and buildings has become one heat pump is not a drop-in replacement for gas-boilers [5]. The UK is committed to If the heat pump is installed in poorly performed or leaky reaching net-zero emissions by 2050 [1]. The support includes buildings, the efficiency will decrease.

Almost all Machine Learning (ML) algorithms comprise a set of hyper-parameters that control their learning process and the quality of their resulting models. The number of hidden units, the learning rate, the minibatch sizes, etc. in neural networks; the kernel parameters and regularization penalty amount in support vector machines; and maximum depth, samples split criteria, and the number of used features in decision trees are few common hyper-parameter examples that need to be configured for the corresponding learning algorithms. Assuming a specific ML algorithm and a dataset, one can build countless number of models, each with potentially different performance and/or learning speeds, by assigning different values to the algorithm's hyper-parameters. While they provide ultimate flexibility in using ML algorithms in different scenarios, they also account for most failures and tedious development procedures. Unsurprisingly, there are numerous studies and practices in the machine learning community devoted to the optimization of hyperparameter. The most straightforward yet difficult approach utilizes expert knowledge to identify potentially better candidates in hyper-parameter search spaces to evaluate and use. The availability of expert knowledge and generating reproducible results are among the primary limitation of such manual searching technique [1], particularly due to the fact that using any learning algorithm on different datasets likely requires different sets of hyper-parameter values [2].

The problem of model selection with a limited number of experimental trials has received considerable attention in cognitive science, where the role of experiments is to discriminate between theories expressed as computational models. Research on this subject has mostly been restricted to optimal experiment design with analytically tractable models. However, cognitive models of increasing complexity, with intractable likelihoods, are becoming more commonplace. In this paper, we propose BOSMOS: an approach to experimental design that can select between computational models without tractable likelihoods. It does so in a data-efficient manner, by sequentially and adaptively generating informative experiments. In contrast to previous approaches, we introduce a novel simulator-based utility objective for design selection, and a new approximation of the model likelihood for model selection. In simulated experiments, we demonstrate that the proposed BOSMOS technique can accurately select models in up to 2 orders of magnitude less time than existing LFI alternatives for three cognitive science tasks: memory retention, sequential signal detection and risky choice.

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.

Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit stochastic gradient descent (ISGD) method to train PINNs for improving the stability of training process. We heuristically analyze how ISGD overcome stiffness in the gradient flow dynamics of PINNs, especially for problems with multi-scale solutions. We theoretically prove that for two-layer fully connected neural networks with large hidden nodes, randomly initialized ISGD converges to a globally optimal solution for the quadratic loss function. Empirical results demonstrate that ISGD works well in practice and compares favorably to other gradient-based optimization methods such as SGD and Adam, while can also effectively address the numerical stiffness in training dynamics via gradient descent.

We consider the problem of optimizing expensive black-box functions over high-dimensional combinatorial spaces which arises in many science, engineering, and ML applications. We use Bayesian Optimization (BO) and propose a novel surrogate modeling approach for efficiently handling a large number of binary and categorical parameters. The key idea is to select a number of discrete structures from the input space (the dictionary) and use them to define an ordinal embedding for high-dimensional combinatorial structures. This allows us to use existing Gaussian process models for continuous spaces. We develop a principled approach based on binary wavelets to construct dictionaries for binary spaces, and propose a randomized construction method that generalizes to categorical spaces. We provide theoretical justification to support the effectiveness of the dictionary-based embeddings. Our experiments on diverse real-world benchmarks demonstrate the effectiveness of our proposed surrogate modeling approach over state-of-the-art BO methods.

The softmax function is a ubiquitous component at the output of neural networks and increasingly in intermediate layers as well. This paper provides convex lower bounds and concave upper bounds on the softmax function, which are compatible with convex optimization formulations for characterizing neural networks and other ML models. We derive bounds using both a natural exponential-reciprocal decomposition of the softmax as well as an alternative decomposition in terms of the log-sum-exp function. The new bounds are provably and/or numerically tighter than linear bounds obtained in previous work on robustness verification of transformers. As illustrations of the utility of the bounds, we apply them to verification of transformers as well as of the robustness of predictive uncertainty estimates of deep ensembles.