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Gaussian approximations are routinely employed in Bayesian statistics to ease inference when the target posterior is intractable. Although these approximations are asymptotically justified by Bernstein-von Mises type results, in practice the expected Gaussian behavior may poorly represent the shape of the posterior, thus affecting approximation accuracy. Motivated by these considerations, we derive an improved class of closed-form approximations of posterior distributions which arise from a new treatment of a third-order version of the Laplace method yielding approximations in a tractable family of skew-symmetric distributions. Under general assumptions which account for misspecified models and non-i.i.d. settings, this family of approximations is shown to have a total variation distance from the target posterior whose rate of convergence improves by at least one order of magnitude the one established by the classical Bernstein-von Mises theorem. Specializing this result to the case of regular parametric models shows that the same improvement in approximation accuracy can be also derived for polynomially bounded posterior functionals. Unlike other higher-order approximations, our results prove that it is possible to derive closed-form and valid densities which are expected to provide, in practice, a more accurate, yet similarly-tractable, alternative to Gaussian approximations of the target posterior, while inheriting its limiting frequentist properties. We strengthen such arguments by developing a practical skew-modal approximation for both joint and marginal posteriors that achieves the same theoretical guarantees of its theoretical counterpart by replacing the unknown model parameters with the corresponding MAP estimate. Empirical studies confirm that our theoretical results closely match the remarkable performance observed in practice, even in finite, possibly small, sample regimes.

This study explores the capabilities of prompt-driven Large Language Models (LLMs) like ChatGPT and GPT-4 in adhering to human guidelines for dialogue summarization. Experiments employed DialogSum (English social conversations) and DECODA (French call center interactions), testing various prompts: including prompts from existing literature and those from human summarization guidelines, as well as a two-step prompt approach. Our findings indicate that GPT models often produce lengthy summaries and deviate from human summarization guidelines. However, using human guidelines as an intermediate step shows promise, outperforming direct word-length constraint prompts in some cases. The results reveal that GPT models exhibit unique stylistic tendencies in their summaries. While BERTScores did not dramatically decrease for GPT outputs suggesting semantic similarity to human references and specialised pre-trained models, ROUGE scores reveal grammatical and lexical disparities between GPT-generated and human-written summaries. These findings shed light on the capabilities and limitations of GPT models in following human instructions for dialogue summarization.

Digital technologies can augment civic participation by facilitating the expression of detailed political preferences. Yet, digital participation efforts often rely on methods optimized for elections involving a few candidates. Here we present data collected in an online experiment where participants built personalized government programs by combining policies proposed by the candidates of the 2022 French and Brazilian presidential elections. We use this data to explore aggregates complementing those used in social choice theory, finding that a metric of divisiveness, which is uncorrelated with traditional aggregation functions, can identify polarizing proposals. These metrics provide a score for the divisiveness of each proposal that can be estimated in the absence of data on the demographic characteristics of participants and that explains the issues that divide a population. These findings suggest divisiveness metrics can be useful complements to traditional aggregation functions in direct forms of digital participation.

Confounder selection, namely choosing a set of covariates to control for confounding between a treatment and an outcome, is arguably the most important step in the design of observational studies. Previous methods, such as Pearl's celebrated back-door criterion, typically require pre-specifying a causal graph, which can often be difficult in practice. We propose an interactive procedure for confounder selection that does not require pre-specifying the graph or the set of observed variables. This procedure iteratively expands the causal graph by finding what we call "primary adjustment sets" for a pair of possibly confounded variables. This can be viewed as inverting a sequence of latent projections of the underlying causal graph. Structural information in the form of primary adjustment sets is elicited from the user, bit by bit, until either a set of covariates are found to control for confounding or it can be determined that no such set exists. Other information, such as the causal relations between confounders, is not required by the procedure. We show that if the user correctly specifies the primary adjustment sets in every step, our procedure is both sound and complete.

Feature attribution is a fundamental task in both machine learning and data analysis, which involves determining the contribution of individual features or variables to a model's output. This process helps identify the most important features for predicting an outcome. The history of feature attribution methods can be traced back to General Additive Models (GAMs), which extend linear regression models by incorporating non-linear relationships between dependent and independent variables. In recent years, gradient-based methods and surrogate models have been applied to unravel complex Artificial Intelligence (AI) systems, but these methods have limitations. GAMs tend to achieve lower accuracy, gradient-based methods can be difficult to interpret, and surrogate models often suffer from stability and fidelity issues. Furthermore, most existing methods do not consider users' contexts, which can significantly influence their preferences. To address these limitations and advance the current state-of-the-art, we define a novel feature attribution framework called Context-Aware Feature Attribution Through Argumentation (CA-FATA). Our framework harnesses the power of argumentation by treating each feature as an argument that can either support, attack or neutralize a prediction. Additionally, CA-FATA formulates feature attribution as an argumentation procedure, and each computation has explicit semantics, which makes it inherently interpretable. CA-FATA also easily integrates side information, such as users' contexts, resulting in more accurate predictions.

signSGD is popular in nonconvex optimization due to its communication efficiency. Yet, existing analyses of signSGD rely on assuming that data are sampled with replacement in each iteration, contradicting the practical implementation where data are randomly reshuffled and sequentially fed into the algorithm. We bridge this gap by proving the first convergence result of signSGD with random reshuffling (SignRR) for nonconvex optimization. Given the dataset size $n$, the number of epochs of data passes $T$, and the variance bound of a stochastic gradient $\sigma^2$, we show that SignRR has the same convergence rate $O(\log(nT)/\sqrt{nT} + \|\sigma\|_1)$ as signSGD \citep{bernstein2018signsgd}. We then present SignRVR and SignRVM, which leverage variance-reduced gradients and momentum updates respectively, both converging at $O(\log(nT)/\sqrt{nT})$. In contrast with the analysis of signSGD, our results do not require an extremely large batch size in each iteration to be of the same order as the total number of iterations \citep{bernstein2018signsgd} or the signs of stochastic and true gradients match element-wise with a minimum probability of 1/2 \citep{safaryan2021stochastic}. We also extend our algorithms to cases where data are distributed across different machines, yielding dist-SignRVR and dist-SignRVM, both converging at $O(\log(n_0T)/\sqrt{n_0T})$, where $n_0$ is the dataset size of a single machine. We back up our theoretical findings through experiments on simulated and real-world problems, verifying that randomly reshuffled sign methods match or surpass existing baselines.

Semantic communication, rather than on a bit-by-bit recovery of the transmitted messages, focuses on the meaning and the goal of the communication itself. In this paper, we propose a novel semantic image coding scheme that preserves the semantic content of an image, while ensuring a good trade-off between coding rate and image quality. The proposed Semantic-Preserving Image Coding based on Conditional Diffusion Models (SPIC) transmitter encodes a Semantic Segmentation Map (SSM) and a low-resolution version of the image to be transmitted. The receiver then reconstructs a high-resolution image using a Denoising Diffusion Probabilistic Models (DDPM) doubly conditioned to the SSM and the low-resolution image. As shown by the numerical examples, compared to state-of-the-art (SOTA) approaches, the proposed SPIC exhibits a better balance between the conventional rate-distortion trade-off and the preservation of semantically-relevant features.

Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper, we introduce a framework for answering this question both intuitively and quantitatively. The underlying structure of the framework is a race between quantum and classical computers, where their relative strengths determine when each wins. While classical computers operate faster, quantum computers can sometimes run more efficient algorithms. Whether the speed advantage or the algorithmic advantage dominates determines whether a problem will benefit from quantum computing or not. Our analysis reveals that many problems, particularly those of small to moderate size that can be important for typical businesses, will not benefit from quantum computing. Conversely, larger problems or those with particularly big algorithmic gains will benefit from near-term quantum computing. Since very large algorithmic gains are rare in practice and theorized to be rare even in principle, our analysis suggests that the benefits from quantum computing will flow either to users of these rare cases, or practitioners processing very large data.

We introduce a Bayesian conditional autoregressive model for analyzing patient-specific and neighborhood risks of stillbirth and preterm birth within a city. Our fully Bayesian approach automatically learns the amount of spatial heterogeneity and spatial dependence between neighborhoods. Our model provides meaningful inferences and uncertainty quantification for both covariate effects and neighborhood risk probabilities through their posterior distributions. We apply our methodology to data from the city of Philadelphia. Using electronic health records (45,919 deliveries at hospitals within the University of Pennsylvania Health System) and United States Census Bureau data from 363 census tracts in Philadelphia, we find that both patient-level characteristics (e.g. self-identified race/ethnicity) and neighborhood-level characteristics (e.g. violent crime) are highly associated with patients' odds of stillbirth or preterm birth. Our neighborhood risk analysis further reveals that census tracts in West Philadelphia and North Philadelphia are at highest risk of these outcomes. Specifically, neighborhoods with higher rates of women in poverty or on public assistance have greater neighborhood risk for these outcomes, while neighborhoods with higher rates of college-educated women or women in the labor force have lower risk. Our findings could be useful for targeted individual and neighborhood interventions.