In this paper, we present a dual representation of the influence functions, whose computational complexity scales with dataset size rather than model size. Both analytically and experimentally, we show that this representation can be an efficient alternative to the original influence functions for estimating changes in parameters, model outputs and loss due to data point removal, when model size is large relative to dataset size, or when evaluating the original influence functions in parameter space is infeasible. The dual representation, however, is limited to linearizable models, which are models whose behavior can be approximated by their linearizations throughout training, and requires materializing a matrix, whose size grows with the product of model output dimension and dataset size.

This paper develops a unified perspective on several stochastic optimal control formulations through the lens of Kullback-Leibler regularization. We propose a central problem that separates the KL penalties on policies and transitions, assigning them independent weights, thereby generalizing the standard trajectory-level KL-regularization commonly used in probabilistic and KL-regularized control. This generalized formulation acts as a generative structure allowing to recover various control problems. These include the classical Stochastic Optimal Control (SOC), Risk-Sensitive Optimal Control (RSOC), and their policy-based KL-regularized counterparts. The latter we refer to as soft-policy SOC and RSOC, facilitating alternative problems with tractable solutions. Beyond serving as regularized variants, we show that these soft-policy formulations majorize the original SOC and RSOC problem. This means that the regularized solution can be iterated to retrieve the original solution. Furthermore, we identify a structurally synchronized case of the risk-seeking soft-policy RSOC formulation, wherein the policy and transition KL-regularization weights coincide. Remarkably, this specific setting gives rise to several powerful properties such as a linear Bellman equation, path integral solution, and, compositionality, thereby extending these computationally favourable properties to a broad class of control problems.

In this work, we introduce dual goal representations for goal-conditioned reinforcement learning (GCRL). A dual goal representation characterizes a state by "the set of temporal distances from all other states"; in other words, it encodes a state through its relations to every other state, measured by temporal distance. This representation provides several appealing theoretical properties. First, it depends only on the intrinsic dynamics of the environment and is invariant to the original state representation. Second, it contains provably sufficient information to recover an optimal goal-reaching policy, while being able to filter out exogenous noise. Based on this concept, we develop a practical goal representation learning method that can be combined with any existing GCRL algorithm. Through diverse experiments on the OGBench task suite, we empirically show that dual goal representations consistently improve offline goal-reaching performance across 20 state- and pixel-based tasks.

A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of instances in the form of convex combinations of extreme points of a produced polytope. Instead of perturbing new instances in the Euclidean feature space, vectors of convex combination coefficients are uniformly generated from the unit simplex, and they form a new dual dataset. A dual linear surrogate model is trained on the dual dataset. The explanation feature importance values are computed by means of simple matrix calculations. The approach can be regarded as a modification of the well-known model LIME. The dual representation inherently allows us to get the example-based explanation. The neural additive model is also considered as a tool for implementing the example-based explanation approach. Many numerical experiments with real datasets are performed for studying the approach. The code of proposed algorithms is available.

Audio-based classification techniques on body sounds have long been studied to aid in the diagnosis of respiratory diseases. While most research is centered on the use of cough as the main biomarker, other body sounds also have the potential to detect respiratory diseases. Recent studies on COVID-19 have shown that breath and speech sounds, in addition to cough, correlate with the disease. Our study proposes Fused Audio Instance and Representation (FAIR) as a method for respiratory disease detection. FAIR relies on constructing a joint feature vector from various body sounds represented in waveform and spectrogram form. We conducted experiments on the use case of COVID-19 detection by combining waveform and spectrogram representation of body sounds. Our findings show that the use of self-attention to combine extracted features from cough, breath, and speech sounds leads to the best performance with an Area Under the Receiver Operating Characteristic Curve (AUC) score of 0.8658, a sensitivity of 0.8057, and a specificity of 0.7958. Compared to models trained solely on spectrograms or waveforms, the use of both representations results in an improved AUC score, demonstrating that combining spectrogram and waveform representation helps to enrich the extracted features and outperforms the models that use only one representation.

In the context of deep learning with kernel machines, the deep Restricted Kernel Machine (DRKM) framework allows multiple levels of kernel PCA (KPCA) and Least-Squares Support Vector Machines (LSSVM) to be combined into a deep architecture using visible and hidden units. We propose a new method for DRKM classification coupling the objectives of KPCA and classification levels, with the hidden feature matrix lying on the Stiefel manifold. The classification level can be formulated as an LSSVM or as an MLP feature map, combining depth in terms of levels and layers. The classification level is expressed in its primal formulation, as the deep KPCA levels, in their dual formulation, can embed the most informative components of the data in a much lower dimensional space. The dual setting is independent of the dimension of the inputs and the primal setting is parametric, which makes the proposed method computationally efficient for both high-dimensional inputs and large datasets. In the experiments, we show that our developed algorithm can effectively learn from small datasets, while using less memory than the convolutional neural network (CNN) with high-dimensional data. and that models with multiple KPCA levels can outperform models with a single level. On the tested larger-scale datasets, DRKM is more energy efficient than CNN while maintaining comparable performance.

In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the fairness properties of primal optima and associated risk allocations. The algorithms we provide allow for learning primal optimizers, optima for the dual representation and corresponding fair risk allocations. We test our algorithms by comparison to a benchmark model, based on a paired exponential utility function, for which we can provide explicit formulas. We also show evidence of convergence in a case for which explicit formulas are not available.

Multi-view data are commonly encountered in data mining applications. Effective extraction of information from multi-view data requires specific design of clustering methods to cater for data with multiple views, which is non-trivial and challenging. In this paper, we propose a novel one-step multi-view clustering method by exploiting the dual representation of both the common and specific information of different views. The motivation originates from the rationale that multi-view data contain not only the consistent knowledge between views but also the unique knowledge of each view. Meanwhile, to make the representation learning more specific to the clustering task, a one-step learning framework is proposed to integrate representation learning and clustering partition as a whole. With this framework, the representation learning and clustering partition mutually benefit each other, which effectively improve the clustering performance. Results from extensive experiments conducted on benchmark multi-view datasets clearly demonstrate the superiority of the proposed method.

We develop a regression based primal-dual martingale approach for solving finite time horizon MDPs with general state and action space. As a result, our method allows for the construction of tight upper and lower biased approximations of the value functions, and, provides tight approximations to the optimal policy. In particular, we prove tight error bounds for the estimated duality gap featuring polynomial dependence on the time horizon, and sublinear dependence on the cardinality/dimension of the possibly infinite state and action space. From a computational point of view the proposed method is efficient since, in contrast to usual duality-based methods for optimal control problems in the literature, the Monte Carlo procedures here involved do not require nested simulations.

Contrastive learning applied to self-supervised representation learning has seen a resurgence in deep models. In this paper, we find that existing contrastive learning based solutions for self-supervised video recognition focus on inter-variance encoding but ignore the intra-variance existing in clips within the same video. We thus propose to learn dual representations for each clip which (i) encode intra-variance through a shuffle-rank pretext task; (ii) encode inter-variance through a temporal coherent contrastive loss. Experiment results show that our method plays an essential role in balancing inter and intra variances and brings consistent performance gains on multiple backbones and contrastive learning frameworks. Integrated with SimCLR and pretrained on Kinetics-400, our method achieves 82.0% and 51.2% downstream classification accuracy on UCF101 and HMDB51 test sets respectively and 46.1% video retrieval accuracy on UCF101, outperforming both pretext-task based and contrastive learning based counterparts.