Due to the progressive advancement of trustworthy machine learning algorithms, fairness in recommender systems is attracting increasing attention and is often considered from the perspective of users. Conventional fairness-aware recommendation models assume that user preferences remain the same between the training set and the testing set. However, this assumption is arguable in reality, where user preference can shift in the testing set due to the natural spatial or temporal heterogeneity. It is concerning that conventional fairness-aware models may be unaware of such distribution shifts, leading to a sharp decline in the model performance. To address the distribution shift problem, we propose a robust fairness-aware recommendation framework based on Distributionally Robust Optimization (DRO) technique. In specific, we assign learnable weights for each sample to approximate the distributions that leads to the worst-case model performance, and then optimize the fairness-aware recommendation model to improve the worst-case performance in terms of both fairness and recommendation accuracy. By iteratively updating the weights and the model parameter, our framework can be robust to unseen testing sets. To ease the learning difficulty of DRO, we use a hard clustering technique to reduce the number of learnable sample weights. To optimize our framework in a full differentiable manner, we soften the above clustering strategy. Empirically, we conduct extensive experiments based on four real-world datasets to verify the effectiveness of our proposed framework.

We have addressed the seismic impedance inversion problem, which is often ill posed because of inaccurate and insufficient data. The approach taken is based on dictionary learning and sparse representation. By shifting a patch window of fixed size on all well-log data, a large number of small overlapping patches are generated. Then regarding these patches as a training set and using K-singular value decomposition algorithm, we obtain a dictionary that describes the common features of subsurface models within the current survey area. On the basis of the assumption that the subsurface geology has similarity and lateral continuity to some extent, the dictionary is used to approximate each model via sparse representations over the learned dictionary. In particular, we impose the sparse representations as additional constraints into the inversion procedure, leading to a well-defined objective function that can not only fit the observed seismic data but also honor the features of the well-log data. We adopt a coordinate descent strategy to solve this objective function. Meanwhile, to enforce lateral continuity in the inverted models, we use an additional stage in which we use the nonlocal similarity information that is extracted from seismic data as spatial coherent prior knowledge to refine the estimated models. Compared with several traditional impedance inversion methods, our algorithm can produce solutions of much higher quality qualitatively and quantitatively.

Extracting horizons from a seismic image has been playing an important role in seismic interpretation. However, how to fully use global-level information contained in the seismic images such as the order of horizon sequences is not well-studied in existing works. To address this issue, we have developed a novel method based on a directed and colored graph, which encodes effective context information for horizon extraction. Following the commonly used framework, which generates horizon patches and then groups them into horizons, we first build a directed and colored graph by representing horizon patches as vertices. In addition, edges in the graph encode the relative spatial positions of horizon patches. This graph explicitly captures the geologic context, which guides the grouping of the horizon patches. Then, we conduct premerging to group horizon patches through matching some predefined subgraph patterns that are designed to capture some special spatial distributions of horizon patches. Finally, we have developed an ordered clustering method to group the rest of the horizon patches into horizons based on the pairwise similarities of horizon patches while preserving geologic reasonability. Experiments on real seismic data indicate that our method can outperform the autotracking approach solely based on the similarity of local waveforms and can correctly pick the horizons even across the fault without any crossing, which demonstrates the effectiveness of exploring the spatial information, i.e., the order of horizon sequences and special spatial distribution of horizon patches.

Seismic facies analysis based on prestack data is becoming popular. Vertical elastic transitions produce the spatial structure variation of prestack waveforms, whereas lateral elastic transitions produce the amplitude intensity variation. In stratigraphic seismic facies analysis, more attention should be paid to waveform spatial structure than amplitude intensity. Conventional classification methods based on distance metrics are difficult to adapt to stratigraphic seismic facies analysis because a distance metric is a comprehensive measure of waveform structure and amplitude intensity. We have developed a dictionary learning (DL) method for prestack seismic facies analysis. The method first learns several dictionaries from labeled prestack waveform data, and these dictionaries consist of several normalization vector bases. The prestack waveform spatial structure is, therefore, embedded in these learned dictionaries, and the amplitude intensity is eliminated by the normalization process. Afterward, these dictionaries are used to sparsely represent prestack seismic data. Seismic facies are classified and determined according to representation error. A source error separation method is used to improve the antinoise performance of DL by iteratively segmenting the noise out in the training data. The results on synthetic and field seismic data show that the proposed method has a stronger tolerance to noise than K singular value decomposition, and the obtained seismic facies boundary is more accurate and clearer than the support vector machine and k-nearest neighbors algorithm. This demonstrates that the proposed method is an effective seismic facies analysis technique.