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We consider the setting of online convex optimization (OCO) with \textit{exp-concave} losses. The best regret bound known for this setting is $O(n\log{}T)$, where $n$ is the dimension and $T$ is the number of prediction rounds (treating all other quantities as constants and assuming $T$ is sufficiently large), and is attainable via the well-known Online Newton Step algorithm (ONS). However, ONS requires on each iteration to compute a projection (according to some matrix-induced norm) onto the feasible convex set, which is often computationally prohibitive in high-dimensional settings and when the feasible set admits a non-trivial structure. In this work we consider projection-free online algorithms for exp-concave and smooth losses, where by projection-free we refer to algorithms that rely only on the availability of a linear optimization oracle (LOO) for the feasible set, which in many applications of interest admits much more efficient implementations than a projection oracle. We present an LOO-based ONS-style algorithm, which using overall $O(T)$ calls to a LOO, guarantees in worst case regret bounded by $\widetilde{O}(n^{2/3}T^{2/3})$ (ignoring all quantities except for $n,T$). However, our algorithm is most interesting in an important and plausible low-dimensional data scenario: if the gradients (approximately) span a subspace of dimension at most $\rho$, $\rho << n$, the regret bound improves to $\widetilde{O}(\rho^{2/3}T^{2/3})$, and by applying standard deterministic sketching techniques, both the space and average additional per-iteration runtime requirements are only $O(\rho{}n)$ (instead of $O(n^2)$). This improves upon recently proposed LOO-based algorithms for OCO which, while having the same state-of-the-art dependence on the horizon $T$, suffer from regret/oracle complexity that scales with $\sqrt{n}$ or worse.

Online changepoint detection algorithms that are based on likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time $T$, it involves considering $O(T)$ possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to $O(\log T)$. This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time $T$ to approximately $\log T$. We show that if one wishes to perform the likelihood ratio test for a different one-parameter exponential family model, then exactly the same pruning rule can be used, and again one need only consider approximately $\log T$ locations at iteration $T$. Furthermore, we show how we can adaptively perform the maximisation step of the algorithm so that we need only maximise the test statistic over a small subset of these possible locations. Empirical results show that the resulting online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average.

The identification of choice models is crucial for understanding consumer behavior and informing marketing or operational strategies, policy design, and product development. The identification of parametric choice-based demand models is typically straightforward. However, nonparametric models, which are highly effective and flexible in explaining customer choice, may encounter the challenge of the dimensionality curse, hindering their identification. A prominent example of a nonparametric model is the ranking-based model, which mirrors the random utility maximization (RUM) class and is known to be nonidentifiable from the collection of choice probabilities alone. Our objective in this paper is to develop a new class of nonparametric models that is not subject to the problem of nonidentifiability. Our model assumes bounded rationality of consumers, which results in symmetric demand cannibalization and intriguingly enables full identification. Additionally, our choice model demonstrates competitive prediction accuracy compared to the state-of-the-art benchmarks in a real-world case study, despite incorporating the assumption of bounded rationality which could, in theory, limit the representation power of our model. In addition, we tackle the important problem of finding the optimal assortment under the proposed choice model. We demonstrate the NP-hardness of this problem and provide a fully polynomial-time approximation scheme through dynamic programming. Additionally, we propose an efficient estimation framework using a combination of column generation and expectation-maximization algorithms, which proves to be more tractable than the estimation algorithm of the aforementioned ranking-based model.

In day-ahead electricity markets based on uniform marginal pricing, small variations in the offering and bidding curves may substantially modify the resulting market outcomes. In this work, we deal with the problem of finding the optimal offering curve for a risk-averse profit-maximizing generating company (GENCO) in a data-driven context. In particular, a large GENCO's market share may imply that her offering strategy can alter the marginal price formation, which can be used to increase profit. We tackle this problem from a novel perspective. First, we propose a optimization-based methodology to summarize each GENCO's step-wise supply curves into a subset of representative price-energy blocks. Then, the relationship between the market price and the resulting energy block offering prices is modeled through a Bayesian linear regression approach, which also allows us to generate stochastic scenarios for the sensibility of the market towards the GENCO strategy, represented by the regression coefficient probabilistic distributions. Finally, this predictive model is embedded in the stochastic optimization model by employing a constraint learning approach. Results show how allowing the GENCO to deviate from her true marginal costs renders significant changes in her profits and the market marginal price. Furthermore, these results have also been tested in an out-of-sample validation setting, showing how this optimal offering strategy is also effective in a real-world market contest.

We present the parametric method SemSimp aimed at measuring semantic similarity of digital resources. SemSimp is based on the notion of information content, and it leverages a reference ontology and taxonomic reasoning, encompassing different approaches for weighting the concepts of the ontology. In particular, weights can be computed by considering either the available digital resources or the structure of the reference ontology of a given domain. SemSimp is assessed against six representative semantic similarity methods for comparing sets of concepts proposed in the literature, by carrying out an experimentation that includes both a statistical analysis and an expert judgement evaluation. To the purpose of achieving a reliable assessment, we used a real-world large dataset based on the Digital Library of the Association for Computing Machinery (ACM), and a reference ontology derived from the ACM Computing Classification System (ACM-CCS). For each method, we considered two indicators. The first concerns the degree of confidence to identify the similarity among the papers belonging to some special issues selected from the ACM Transactions on Information Systems journal, the second the Pearson correlation with human judgement. The results reveal that one of the configurations of SemSimp outperforms the other assessed methods. An additional experiment performed in the domain of physics shows that, in general, SemSimp provides better results than the other similarity methods.

Within medical imaging segmentation, the Dice coefficient and Hausdorff-based metrics are standard measures of success for deep learning models. However, modern loss functions for medical image segmentation often only consider the Dice coefficient or similar region-based metrics during training. As a result, segmentation architectures trained over such loss functions run the risk of achieving high accuracy for the Dice coefficient but low accuracy for Hausdorff-based metrics. Low accuracy on Hausdorff-based metrics can be problematic for applications such as tumor segmentation, where such benchmarks are crucial. For example, high Dice scores accompanied by significant Hausdorff errors could indicate that the predictions fail to detect small tumors. We propose the Weighted Normalized Boundary Loss, a novel loss function to minimize Hausdorff-based metrics with more desirable numerical properties than current methods and with weighting terms for class imbalance. Our loss function outperforms other losses when tested on the BraTS dataset using a standard 3D U-Net and the state-of-the-art nnUNet architectures. These results suggest we can improve segmentation accuracy with our novel loss function.

We consider a dynamic pricing problem for repeated contextual second-price auctions with multiple strategic buyers who aim to maximize their long-term time discounted utility. The seller has limited information on buyers' overall demand curves which depends on a non-parametric market-noise distribution, and buyers may potentially submit corrupted bids (relative to true valuations) to manipulate the seller's pricing policy for more favorable reserve prices in the future. We focus on designing the seller's learning policy to set contextual reserve prices where the seller's goal is to minimize regret compared to the revenue of a benchmark clairvoyant policy that has full information of buyers' demand. We propose a policy with a phased-structure that incorporates randomized "isolation" periods, during which a buyer is randomly chosen to solely participate in the auction. We show that this design allows the seller to control the number of periods in which buyers significantly corrupt their bids. We then prove that our policy enjoys a $T$-period regret of $\widetilde{\mathcal{O}}(\sqrt{T})$ facing strategic buyers. Finally, we conduct numerical simulations to compare our proposed algorithm to standard pricing policies. Our numerical results show that our algorithm outperforms these policies under various buyer bidding behavior.

Consider two $D$-dimensional data vectors (e.g., embeddings): $u, v$. In many embedding-based retrieval (EBR) applications where the vectors are generated from trained models, $D=256\sim 1024$ are common. In this paper, OPORP (one permutation + one random projection) uses a variant of the ``count-sketch'' type of data structures for achieving data reduction/compression. With OPORP, we first apply a permutation on the data vectors. A random vector $r$ is generated i.i.d. with moments: $E(r_i) = 0, E(r_i^2)=1, E(r_i^3) =0, E(r_i^4)=s$. We multiply (as dot product) $r$ with all permuted data vectors. Then we break the $D$ columns into $k$ equal-length bins and aggregate (i.e., sum) the values in each bin to obtain $k$ samples from each data vector. One crucial step is to normalize the $k$ samples to the unit $l_2$ norm. We show that the estimation variance is essentially: $(s-1)A + \frac{D-k}{D-1}\frac{1}{k}\left[ (1-\rho^2)^2 -2A\right]$, where $A\geq 0$ is a function of the data ($u,v$). This formula reveals several key properties: (1) We need $s=1$. (2) The factor $\frac{D-k}{D-1}$ can be highly beneficial in reducing variances. (3) The term $\frac{1}{k}(1-\rho^2)^2$ is actually the asymptotic variance of the classical correlation estimator. We illustrate that by letting the $k$ in OPORP to be $k=1$ and repeat the procedure $m$ times, we exactly recover the work of ``very spars random projections'' (VSRP). This immediately leads to a normalized estimator for VSRP which substantially improves the original estimator of VSRP. In summary, with OPORP, the two key steps: (i) the normalization and (ii) the fixed-length binning scheme, have considerably improved the accuracy in estimating the cosine similarity, which is a routine (and crucial) task in modern embedding-based retrieval (EBR) applications.

Low-dose Computed Tomography (LDCT) reconstruction is an important task in medical image analysis. Recent years have seen many deep learning based methods, proved to be effective in this area. However, these methods mostly follow a supervised architecture, which needs paired CT image of full dose and quarter dose, and the solution is highly dependent on specific measurements. In this work, we introduce Denoising Diffusion LDCT Model, dubbed as DDLM, generating noise-free CT image using conditioned sampling. DDLM uses pretrained model, and need no training nor tuning process, thus our proposal is in unsupervised manner. Experiments on LDCT images have shown comparable performance of DDLM using less inference time, surpassing other state-of-the-art methods, proving both accurate and efficient. Implementation code will be set to public soon.

In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model instead. In this work, we propose a prior on the model fit, as measured by a Bayesian coefficient of determination (R2), which then induces a prior on the individual parameters. We achieve this by placing a beta prior on R2 and then deriving the induced prior on the global variance parameter for generalized linear mixed models. We derive closed-form expressions in many scenarios and present several approximation strategies when an analytic form is not possible and/or to allow for easier computation. In these situations, we suggest approximating the prior by using a generalized beta prime distribution and provide a simple default prior construction scheme. This approach is quite flexible and can be easily implemented in standard Bayesian software. Lastly, we demonstrate the performance of the method on simulated data, where it particularly shines in high-dimensional examples, as well as real-world data, which shows its ability to model spatial correlation in the random effects.