We study the dynamic joint assortment selection and positioning problem, where the attraction of each product depends on both its intrinsic appeal and its display position under a Multinomial Logit (MNL) choice framework. Our study ranges from the multiplicative position effects model, in which each product's attraction is scaled by a position-specific factor, to a general position effects model assigning independent attraction parameters to every product--position pair to capture heterogeneous synergies. For both models, we design round-based learning algorithms that update decisions after every single feedback, and establish the first regret-optimal characterization. Besides, our round-based algorithms provide the prompt operations needed by modern platforms. For the multiplicative model, we develop a cross-position pairwise maximum likelihood estimator with a clipping mechanism, and prove that our algorithm P2MLE-UCB attains a regret of $\tilde{O}(\sqrt{NT})$, matching the lower bound and closing the $\sqrt{K}$ gap left by prior epoch-based analyses. For the general model, we establish a minimax lower bound and propose GP2-UCB with a matching upper bound. Moreover, we design an efficient subroutine for the per-round joint assortment and positioning optimization based on Dinkelbach's method and maximum-weight bipartite matching. Numerical experiments on synthetic data and the Expedia dataset show that our algorithms consistently outperform state-of-the-art benchmarks.

Online A/B tests have become increasingly popular and important for social platforms.

Online A/B tests have become increasingly popular and important for social platforms.

In this paper we propose a general framework for learning distributed representations of attributes: characteristics of text whose representations can be jointly learned with word embeddings. Attributes can correspond to a wide variety of concepts, such as document indicators (to learn sentence vectors), language indicators (to learn distributed language representations), meta-data and side information (such as the age, gender and industry of a blogger) or representations of authors. We describe a third-order model where word context and attribute vectors interact multiplicatively to predict the next word in a sequence. This leads to the notion of conditional word similarity: how meanings of words change when conditioned on different attributes. We perform several experimental tasks including sentiment classification, cross-lingual document classification, and blog authorship attribution. We also qualitatively evaluate conditional word neighbours and attribute-conditioned text generation.

In this paper we propose a general framework for learning distributed representations of attributes: characteristics of text whose representations can be jointly learned with word embeddings. Attributes can correspond to a wide variety of concepts, such as document indicators (to learn sentence vectors), language indicators (to learn distributed language representations), meta-data and side information (such as the age, gender and industry of a blogger) or representations of authors. We describe a third-order model where word context and attribute vectors interact multiplicatively to predict the next word in a sequence. This leads to the notion of conditional word similarity: how meanings of words change when conditioned on different attributes. We perform several experimental tasks including sentiment classification, cross-lingual document classification, and blog authorship attribution.

Sensor-based human activity recognition is important in daily scenarios such as smart healthcare and homes due to its non-intrusive privacy and low cost advantages, but the problem of out-of-domain generalization caused by differences in focusing individuals and operating environments can lead to significant accuracy degradation on cross-person behavior recognition due to the inconsistent distributions of training and test data. To address the above problems, this paper proposes a new method, Multi-channel Time Series Decomposition Network (MTSDNet). Firstly, MTSDNet decomposes the original signal into a combination of multiple polynomials and trigonometric functions by the trainable parameterized temporal decomposition to learn the low-rank representation of the original signal for improving the extraterritorial generalization ability of the model. Then, the different components obtained by the decomposition are classified layer by layer and the layer attention is used to aggregate components to obtain the final classification result. Extensive evaluation on DSADS, OPPORTUNITY, PAMAP2, UCIHAR and UniMib public datasets shows the advantages in predicting accuracy and stability of our method compared with other competing strategies, including the state-of-the-art ones. And the visualization is conducted to reveal MTSDNet's interpretability and layer-by-layer characteristics.

We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the Baik-Ben Arous-P\'ech\'e (BBP) transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.

Knowledge Base Completion has been a very active area recently, where multiplicative models have generally outperformed additive and other deep learning methods -- like GNN, CNN, path-based models. Several recent KBC papers propose architectural changes, new training methods, or even a new problem reformulation. They evaluate their methods on standard benchmark datasets - FB15k, FB15k-237, WN18, WN18RR, and Yago3-10. Recently, some papers discussed how 1-N scoring can speed up training and evaluation. In this paper, we discuss how by just applying this training regime to a basic model like Complex gives near SOTA performance on all the datasets -- we call this model COMPLEX-V2. We also highlight how various multiplicative methods recently proposed in literature benefit from this trick and become indistinguishable in terms of performance on most datasets. This paper calls for a reassessment of their individual value, in light of these findings.

In this paper we propose a general framework for learning distributed representations of attributes: characteristics of text whose representations can be jointly learned with word embeddings. Attributes can correspond to a wide variety of concepts, such as document indicators (to learn sentence vectors), language indicators (to learn distributed language representations), meta-data and side information (such as the age, gender and industry of a blogger) or representations of authors. We describe a third-order model where word context and attribute vectors interact multiplicatively to predict the next word in a sequence. This leads to the notion of conditional word similarity: how meanings of words change when conditioned on different attributes. We perform several experimental tasks including sentiment classification, cross-lingual document classification, and blog authorship attribution.

Recently, there has been interest in multiplicative recurrent neural networks for language modeling. Indeed, simple Recurrent Neural Networks (RNNs) encounter difficulties recovering from past mistakes when generating sequences due to high correlation between hidden states. These challenges can be mitigated by integrating second-order terms in the hidden-state update. One such model, multiplicative Long Short-Term Memory (mLSTM) is particularly interesting in its original formulation because of the sharing of its second-order term, referred to as the intermediate state. We explore these architectural improvements by introducing new models and testing them on character-level language modeling tasks. This allows us to establish the relevance of shared parametrization in recurrent language modeling.