In modern data analysis, sparse model selection becomes inevitable once the number of predictors variables is very high. It is well-known that model selection procedures like the Lasso or Boosting tend to overfit on real data. The celebrated Stability Selection overcomes these weaknesses by aggregating models, based on subsamples of the training data, followed by choosing a stable predictor set which is usually much sparser than the predictor sets from the raw models. The standard Stability Selection is based on a global criterion, namely the per-family error rate, while additionally requiring expert knowledge to suitably configure the hyperparameters. Since model selection depends on the loss function, i.e., predictor sets selected w.r.t. some particular loss function differ from those selected w.r.t. some other loss function, we propose a Stability Selection variant which respects the chosen loss function via an additional validation step based on out-of-sample validation data, optionally enhanced with an exhaustive search strategy. Our Stability Selection variants are widely applicable and user-friendly. Moreover, our Stability Selection variants can avoid the issue of severe underfitting which affects the original Stability Selection for noisy high-dimensional data, so our priority is not to avoid false positives at all costs but to result in a sparse stable model with which one can make predictions. Experiments where we consider both regression and binary classification and where we use Boosting as model selection algorithm reveal a significant precision improvement compared to raw Boosting models while not suffering from any of the mentioned issues of the original Stability Selection.
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損失函數，在AI中亦稱呼距離函數，度量函數。此處的距離代表的是抽象性的，代表真實數據與預測數據之間的誤差。損失函數（loss function）是用來估量你模型的預測值f(x)與真實值Y的不一致程度，它是一個非負實值函數,通常使用L(Y, f(x))來表示，損失函數越小，模型的魯棒性就越好。損失函數是經驗風險函數的核心部分，也是結構風險函數重要組成部分。
Graph Convolutional Networks (GCNs) are one of the most popular architectures that are used to solve classification problems accompanied by graphical information. We present a rigorous theoretical understanding of the effects of graph convolutions in multi-layer networks. We study these effects through the node classification problem of a non-linearly separable Gaussian mixture model coupled with a stochastic block model. First, we show that a single graph convolution expands the regime of the distance between the means where multi-layer networks can classify the data by a factor of at least $1/\sqrt[4]{\mathbb{E}{\rm deg}}$, where $\mathbb{E}{\rm deg}$ denotes the expected degree of a node. Second, we show that with a slightly stronger graph density, two graph convolutions improve this factor to at least $1/\sqrt[4]{n}$, where $n$ is the number of nodes in the graph. Finally, we provide both theoretical and empirical insights into the performance of graph convolutions placed in different combinations among the layers of a network, concluding that the performance is mutually similar for all combinations of the placement. We present extensive experiments on both synthetic and real-world data that illustrate our results.
Recent progress in deep learning has continuously improved the accuracy of dialogue response selection. In particular, sophisticated neural network architectures are leveraged to capture the rich interactions between dialogue context and response candidates. While remarkably effective, these models also bring in a steep increase in computational cost. Consequently, such models can only be used as a re-rank module in practice. In this study, we present a solution to directly select proper responses from a large corpus or even a nonparallel corpus that only consists of unpaired sentences, using a dense retrieval model. To push the limits of dense retrieval, we design an interaction layer upon the dense retrieval models and apply a set of tailor-designed learning strategies. Our model shows superiority over strong baselines on the conventional re-rank evaluation setting, which is remarkable given its efficiency. To verify the effectiveness of our approach in realistic scenarios, we also conduct full-rank evaluation, where the target is to select proper responses from a full candidate pool that may contain millions of candidates and evaluate them fairly through human annotations. Our proposed model notably outperforms pipeline baselines that integrate fast recall and expressive re-rank modules. Human evaluation results show that enlarging the candidate pool with nonparallel corpora improves response quality further.
Common tasks encountered in epidemiology, including disease incidence estimation and causal inference, rely on predictive modeling. Constructing a predictive model can be thought of as learning a prediction function, i.e., a function that takes as input covariate data and outputs a predicted value. Many strategies for learning these functions from data are available, from parametric regressions to machine learning algorithms. It can be challenging to choose an approach, as it is impossible to know in advance which one is the most suitable for a particular dataset and prediction task at hand. The super learner (SL) is an algorithm that alleviates concerns over selecting the one "right" strategy while providing the freedom to consider many of them, such as those recommended by collaborators, used in related research, or specified by subject-matter experts. It is an entirely pre-specified and data-adaptive strategy for predictive modeling. To ensure the SL is well-specified for learning the prediction function, the analyst does need to make a few important choices. In this Education Corner article, we provide step-by-step guidelines for making these choices, walking the reader through each of them and providing intuition along the way. In doing so, we aim to empower the analyst to tailor the SL specification to their prediction task, thereby ensuring their SL performs as well as possible. A flowchart provides a concise, easy-to-follow summary of key suggestions and heuristics, based on our accumulated experience, and guided by theory.
In this work, we aim to consider the application of contrastive learning in the scenario of the recommendation system adequately, making it more suitable for recommendation task. We propose a learning paradigm called supervised contrastive learning(SCL) to support the graph convolutional neural network. Specifically, we will calculate the similarity between different nodes in user side and item side respectively during data preprocessing, and then when applying contrastive learning, not only will the augmented views be regarded as the positive samples, but also a certain number of similar samples will be regarded as the positive samples, which is different with SimCLR that treats other samples in a batch as negative samples. We apply SCL on the most advanced LightGCN. In addition, in order to consider the uncertainty of node interaction, we also propose a new data augment method called node replication. Empirical research and ablation study on Gowalla, Yelp2018, Amazon-Book datasets prove the effectiveness of SCL and node replication, which improve the accuracy of recommendations and robustness to interactive noise.
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.
Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications in biomolecular modeling and drug discovery, from rapid virtual screening to detailed free energy calculations. Traditionally, MM potentials have relied on human-curated, inflexible, and poorly extensible discrete chemical perception rules or applying parameters to small molecules or biopolymers, making it difficult to optimize both types and parameters to fit quantum chemical or physical property data. Here, we propose an alternative approach that uses graph neural networks to perceive chemical environments, producing continuous atom embeddings from which valence and nonbonded parameters can be predicted using invariance-preserving layers. Since all stages are built from smooth neural functions, the entire process is modular and end-to-end differentiable with respect to model parameters, allowing new force fields to be easily constructed, extended, and applied to arbitrary molecules. We show that this approach is not only sufficiently expressive to reproduce legacy atom types, but that it can learn to accurately reproduce and extend existing molecular mechanics force fields. Trained with arbitrary loss functions, it can construct entirely new force fields self-consistently applicable to both biopolymers and small molecules directly from quantum chemical calculations, with superior fidelity than traditional atom or parameter typing schemes. When trained on the same quantum chemical small molecule dataset used to parameterize the openff-1.2.0 small molecule force field augmented with a peptide dataset, the resulting espaloma model shows superior accuracy vis-\`a-vis experiments in computing relative alchemical free energy calculations for a popular benchmark set.
Response selector is an essential component of generation-based dialogue systems and it aims to pick out an optimal response in a candidate pool to continue the dialogue. The current state-of-the-art methods are mainly based on the encoding paradigm called Cross-Encoder, which separately encodes each context-response pair and ranks the responses according to their fitness scores. However, Cross-Encoder repeatedly encodes the same lengthy context for each response, resulting in high computational costs. Moreover, without considering the relationship among the candidates, it is difficult to figure out which candidate is the best response purely based on the fitness score per candidate. We aim to address these problems through a new paradigm called Panoramic-Encoder. The proposed method encodes all candidates and the context at once and realizes the mutual interaction using a tailored candidate attention mechanism (CAM). It also enables the integration of some effective training techniques, such as the in-batch negative training, which cannot be used in Cross-Encoders. Extensive experiments across four benchmark datasets show that our new method significantly outperforms the current state-of-the-art with lower computational complexity.
Modern optimization strategies such as evolutionary algorithms, ant colony algorithms, Bayesian optimization techniques, etc.~come with several parameters that steer their behavior during the optimization process. To obtain high-performing algorithm instances, automated algorithm configuration techniques have been developed. One of the most popular tools is irace, which evaluates configurations in sequential races, making use of iterated statistical tests to discard poorly performing configurations. At the end of the race, a set of elite configurations are selected from those survivor configurations which were not discarded, using greedy truncation selection. We study two alternative selection methods: one keeps the best survivor and selects the remaining configurations uniformly at random from the set of survivors while the other applies entropy to maximize the diversity of the elites. These methods are tested for tuning ant colony optimization algorithms for traveling salesperson problems and the quadratic assignment problem and tuning an exact tree search solver for satisfiability problems. The experimental results show improvement on the tested benchmarks compared to the default selection of irace. In addition, the obtained results indicate that non-elitist can obtain diverse algorithm configurations, which encourages us to explore a wider range of solutions to understand the behavior of algorithms.
While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based problems. To overcome the lack of permutation-based benchmark problems, we propose a general way to transfer the classic pseudo-Boolean benchmarks into benchmarks defined on sets of permutations. We then conduct a rigorous runtime analysis of the permutation-based $(1+1)$ EA proposed by Scharnow, Tinnefeld, and Wegener (2004) on the analogues of the \textsc{LeadingOnes} and \textsc{Jump} benchmarks. The latter shows that, different from bit-strings, it is not only the Hamming distance that determines how difficult it is to mutate a permutation $\sigma$ into another one $\tau$, but also the precise cycle structure of $\sigma \tau^{-1}$. For this reason, we also regard the more symmetric scramble mutation operator. We observe that it not only leads to simpler proofs, but also reduces the runtime on jump functions with odd jump size by a factor of $\Theta(n)$. Finally, we show that a heavy-tailed version of the scramble operator, as in the bit-string case, leads to a speed-up of order $m^{\Theta(m)}$ on jump functions with jump size~$m$.%
With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
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