In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward $g(\gamma, v)$ depends on the proposed threshold $\gamma$ and latent value $v$ and it can be $only$ achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most $\epsilon$ smaller than the optimum and prove that the number of queries needed can be infinitely large even when $g(\gamma, v)$ is monotone with respect to both $\gamma$ and $v$. On the positive side, we provide a tight query complexity $\tilde{\Theta}(1/\epsilon^3)$ when $g$ is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight $\tilde{\Theta}(1/\epsilon^3)$ query complexity can be achieved as long as $g$ satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight $\Theta(T^{2/3})$ regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.
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In this paper, we focus on the design of binary constant-weight codes that admit low-complexity encoding and decoding algorithms, and that have size as a power of $2$. We construct a family of $(n=2^\ell, M=2^k, d=2)$ constant-weight codes ${\cal C}[\ell, r]$ parameterized by integers $\ell \geq 3$ and $1 \leq r \leq \lfloor \frac{\ell+3}{4} \rfloor$, by encoding information in the gaps between successive $1$'s of a vector. The code has weight $w = \ell$ and combinatorial dimension $k$ that scales quadratically with $\ell$. The encoding time is linear in the input size $k$, and the decoding time is poly-logarithmic in the input size $n$, discounting the linear time spent on parsing the input. Encoding and decoding algorithms of similar codes known in either information-theoretic or combinatorial literature require computation of large number of binomial coefficients. Our algorithms fully eliminate the need to evaluate binomial coefficients. While the code has a natural price to pay in $k$, it performs fairly well against the information-theoretic upper bound $\lfloor \log_2 {n \choose w} \rfloor$. When $\ell =3$, the code is optimal achieving the upper bound; when $\ell=4$, it is one bit away from the upper bound, and as $\ell$ grows it is order-optimal in the sense that the ratio of $k$ with its upper bound becomes a constant $\frac{11}{16}$ when $r=\lfloor \frac{\ell+3}{4} \rfloor$. With the same or even lower complexity, we derive new codes permitting a wider range of parameters by modifying ${\cal C}[\ell, r]$ in two different ways. The code derived using the first approach has the same blocklength $n=2^\ell$, but weight $w$ is allowed to vary from $\ell-1$ to $1$. In the second approach, the weight remains fixed as $w = \ell$, but the blocklength is reduced to $n=2^\ell - 2^r +1$. For certain selected values of parameters, these modified codes have an optimal $k$.
We consider channel coding for discrete memoryless channels (DMCs) with a novel cost constraint that constrains both the mean and the variance of the cost of the codewords. We show that the maximum (asymptotically) achievable rate under the new cost formulation is equal to the capacity-cost function; in particular, the strong converse holds. We further characterize the optimal second-order coding rate of these cost-constrained codes; in particular, the optimal second-order coding rate is finite. We then show that the second-order coding performance is strictly improved with feedback using a new variation of timid/bold coding, significantly broadening the applicability of timid/bold coding schemes from unconstrained compound-dispersion channels to all cost-constrained channels. Equivalent results on the minimum average probability of error are also given.
In this paper, we extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We achieve this by considering monoidal categories that are enriched in the category of Eilenberg-Moore algebras for a monad. Under the condition that this monad is monoidal and affine, we construct an adjunction between symmetric monoidal categories and symmetric monoidal categories enriched over algebras for the monad. This allows us to devise an extension, and its semantics, of the ZX-calculus with probabilistic choices by freely enriching over convex algebras, which are the algebras of the finite distribution monad. We show how this construction can be used for diagrammatic reasoning of noise in quantum systems.
Reconfigurable intelligent surfaces, with their large number of antennas, offer an interesting opportunity for high spatial-resolution imaging. In this paper, we propose a novel RIS-aided integrated imaging and communication system that can reduce the RIS beam training overhead for communication by leveraging the imaging of the surrounding environment. In particular, using the RIS as a wireless imaging device, our system constructs the scene depth map of the environment, including the mobile user. Then, we develop a user detection algorithm that subtracts the background and extracts the mobile user attributes from the depth map. These attributes are then utilized to design the RIS interaction vector and the beam selection strategy with low overhead. Simulation results show that the proposed approach can achieve comparable beamforming gain to the optimal/exhaustive beam selection solution while requiring 1000 times less beam training overhead.
In this paper, we investigate the problem of deciding whether two standard normal random vectors $\mathsf{X}\in\mathbb{R}^{n}$ and $\mathsf{Y}\in\mathbb{R}^{n}$ are correlated or not. This is formulated as a hypothesis testing problem, where under the null hypothesis, these vectors are statistically independent, while under the alternative, $\mathsf{X}$ and a randomly and uniformly permuted version of $\mathsf{Y}$, are correlated with correlation $\rho$. We analyze the thresholds at which optimal testing is information-theoretically impossible and possible, as a function of $n$ and $\rho$. To derive our information-theoretic lower bounds, we develop a novel technique for evaluating the second moment of the likelihood ratio using an orthogonal polynomials expansion, which among other things, reveals a surprising connection to integer partition functions. We also study a multi-dimensional generalization of the above setting, where rather than two vectors we observe two databases/matrices, and furthermore allow for partial correlations between these two.
Consider the supervised learning setting where the goal is to learn to predict labels $\mathbf y$ given points $\mathbf x$ from a distribution. An \textit{omnipredictor} for a class $\mathcal L$ of loss functions and a class $\mathcal C$ of hypotheses is a predictor whose predictions incur less expected loss than the best hypothesis in $\mathcal C$ for every loss in $\mathcal L$. Since the work of [GKR+21] that introduced the notion, there has been a large body of work in the setting of binary labels where $\mathbf y \in \{0, 1\}$, but much less is known about the regression setting where $\mathbf y \in [0,1]$ can be continuous. Our main conceptual contribution is the notion of \textit{sufficient statistics} for loss minimization over a family of loss functions: these are a set of statistics about a distribution such that knowing them allows one to take actions that minimize the expected loss for any loss in the family. The notion of sufficient statistics relates directly to the approximate rank of the family of loss functions. Our key technical contribution is a bound of $O(1/\varepsilon^{2/3})$ on the $\epsilon$-approximate rank of convex, Lipschitz functions on the interval $[0,1]$, which we show is tight up to a factor of $\mathrm{polylog} (1/\epsilon)$. This yields improved runtimes for learning omnipredictors for the class of all convex, Lipschitz loss functions under weak learnability assumptions about the class $\mathcal C$. We also give efficient omnipredictors when the loss families have low-degree polynomial approximations, or arise from generalized linear models (GLMs). This translation from sufficient statistics to faster omnipredictors is made possible by lifting the technique of loss outcome indistinguishability introduced by [GKH+23] for Boolean labels to the regression setting.
Calibrating simulation models that take large quantities of multi-dimensional data as input is a hard simulation optimization problem. Existing adaptive sampling strategies offer a methodological solution. However, they may not sufficiently reduce the computational cost for estimation and solution algorithm's progress within a limited budget due to extreme noise levels and heteroskedasticity of system responses. We propose integrating stratification with adaptive sampling for the purpose of efficiency in optimization. Stratification can exploit local dependence in the simulation inputs and outputs. Yet, the state-of-the-art does not provide a full capability to adaptively stratify the data as different solution alternatives are evaluated. We devise two procedures for data-driven calibration problems that involve a large dataset with multiple covariates to calibrate models within a fixed overall simulation budget. The first approach dynamically stratifies the input data using binary trees, while the second approach uses closed-form solutions based on linearity assumptions between the objective function and concomitant variables. We find that dynamical adjustment of stratification structure accelerates optimization and reduces run-to-run variability in generated solutions. Our case study for calibrating a wind power simulation model, widely used in the wind industry, using the proposed stratified adaptive sampling, shows better-calibrated parameters under a limited budget.
In this paper, we tackle two challenges in multimodal learning for visual recognition: 1) when missing-modality occurs either during training or testing in real-world situations; and 2) when the computation resources are not available to finetune on heavy transformer models. To this end, we propose to utilize prompt learning and mitigate the above two challenges together. Specifically, our modality-missing-aware prompts can be plugged into multimodal transformers to handle general missing-modality cases, while only requiring less than 1% learnable parameters compared to training the entire model. We further explore the effect of different prompt configurations and analyze the robustness to missing modality. Extensive experiments are conducted to show the effectiveness of our prompt learning framework that improves the performance under various missing-modality cases, while alleviating the requirement of heavy model re-training. Code is available.
In this paper, we propose a novel multi-task learning architecture, which incorporates recent advances in attention mechanisms. Our approach, the Multi-Task Attention Network (MTAN), consists of a single shared network containing a global feature pool, together with task-specific soft-attention modules, which are trainable in an end-to-end manner. These attention modules allow for learning of task-specific features from the global pool, whilst simultaneously allowing for features to be shared across different tasks. The architecture can be built upon any feed-forward neural network, is simple to implement, and is parameter efficient. Experiments on the CityScapes dataset show that our method outperforms several baselines in both single-task and multi-task learning, and is also more robust to the various weighting schemes in the multi-task loss function. We further explore the effectiveness of our method through experiments over a range of task complexities, and show how our method scales well with task complexity compared to baselines.
In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.
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