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We consider the problem of model selection when grouping structure is inherent within the regressors. Using a Bayesian approach, we model the mean vector by a one-group global-local shrinkage prior belonging to a broad class of such priors that includes the horseshoe prior. In the context of variable selection, this class of priors was studied by Tang et al. (2018) \cite{tang2018bayesian}. A modified form of the usual class of global-local shrinkage priors with polynomial tail on the group regression coefficients is proposed. The resulting threshold rule selects the active group if within a group, the ratio of the $L_2$ norm of the posterior mean of its group coefficient to that of the corresponding ordinary least square group estimate is greater than a half. In the theoretical part of this article, we have used the global shrinkage parameter either as a tuning one or an empirical Bayes estimate of it depending on the knowledge regarding the underlying sparsity of the model. When the proportion of active groups is known, using $\tau$ as a tuning parameter, we have proved that our method enjoys variable selection consistency. In case this proportion is unknown, we propose an empirical Bayes estimate of $\tau$. Even if this empirical Bayes estimate is used, then also our half-thresholding rule captures the true sparse group structure. Though our theoretical works rely on a special form of the design matrix, but for general design matrices also, our simulation results show that the half-thresholding rule yields results similar to that of Yang and Narisetty (2020) \cite{yang2020consistent}. As a consequence of this, in a high dimensional sparse group selection problem, instead of using the so-called `gold standard' spike and slab prior, one can use the one-group global-local shrinkage priors with polynomial tail to obtain similar results.

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.

Given a computable sequence of natural numbers, it is a natural task to find a G\"odel number of a program that generates this sequence. It is easy to see that this problem is neither continuous nor computable. In algorithmic learning theory this problem is well studied from several perspectives and one question studied there is for which sequences this problem is at least learnable in the limit. Here we study the problem on all computable sequences and we classify the Weihrauch complexity of it. For this purpose we can, among other methods, utilize the amalgamation technique known from learning theory. As a benchmark for the classification we use closed and compact choice problems and their jumps on natural numbers, and we argue that these problems correspond to induction and boundedness principles, as they are known from the Kirby-Paris hierarchy in reverse mathematics. We provide a topological as well as a computability-theoretic classification, which reveal some significant differences.

Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such quantitative reachability properties by generating inductive invariants on source-code level. Our implementation shows promise: It finds invariants for (in)finite-state programs, can beat state-of-the-art probabilistic model checkers, and is competitive with modern tools dedicated to invariant synthesis and expected runtime reasoning.

Learning causal relationships between variables is a fundamental task in causal inference and directed acyclic graphs (DAGs) are a popular choice to represent the causal relationships. As one can recover a causal graph only up to its Markov equivalence class from observations, interventions are often used for the recovery task. Interventions are costly in general and it is important to design algorithms that minimize the number of interventions performed. In this work, we study the problem of identifying the smallest set of interventions required to learn the causal relationships between a subset of edges (target edges). Under the assumptions of faithfulness, causal sufficiency, and ideal interventions, we study this problem in two settings: when the underlying ground truth causal graph is known (subset verification) and when it is unknown (subset search). For the subset verification problem, we provide an efficient algorithm to compute a minimum sized interventional set; we further extend these results to bounded size non-atomic interventions and node-dependent interventional costs. For the subset search problem, in the worst case, we show that no algorithm (even with adaptivity or randomization) can achieve an approximation ratio that is asymptotically better than the vertex cover of the target edges when compared with the subset verification number. This result is surprising as there exists a logarithmic approximation algorithm for the search problem when we wish to recover the whole causal graph. To obtain our results, we prove several interesting structural properties of interventional causal graphs that we believe have applications beyond the subset verification/search problems studied here.

For a given elliptic curve $E$ over a finite local ring, we denote by $E^{\infty}$ its subgroup at infinity. Every point $P \in E^{\infty}$ can be described solely in terms of its $x$-coordinate $P_x$, which can be therefore used to parameterize all its multiples $nP$. We refer to the coefficient of $(P_x)^i$ in the parameterization of $(nP)_x$ as the $i$-th multiplication polynomial. We show that this coefficient is a degree-$i$ rational polynomial without a constant term in $n$. We also prove that no primes greater than $i$ may appear in the denominators of its terms. As a consequence, for every finite field $\mathbb{F}_q$ and any $k\in\mathbb{N}^*$, we prescribe the group structure of a generic elliptic curve defined over $\mathbb{F}_q[X]/(X^k)$, and we show that their ECDLP on $E^{\infty}$ may be efficiently solved.

We analyze to what extent final users can infer information about the level of protection of their data when the data obfuscation mechanism is a priori unknown to them (the so-called ''black-box'' scenario). In particular, we delve into the investigation of two notions of local differential privacy (LDP), namely {\epsilon}-LDP and R\'enyi LDP. On one hand, we prove that, without any assumption on the underlying distributions, it is not possible to have an algorithm able to infer the level of data protection with provable guarantees; this result also holds for the central versions of the two notions of DP considered. On the other hand, we demonstrate that, under reasonable assumptions (namely, Lipschitzness of the involved densities on a closed interval), such guarantees exist and can be achieved by a simple histogram-based estimator. We validate our results experimentally and we note that, on a particularly well-behaved distribution (namely, the Laplace noise), our method gives even better results than expected, in the sense that in practice the number of samples needed to achieve the desired confidence is smaller than the theoretical bound, and the estimation of {\epsilon} is more precise than predicted.

We propose a new approach to portfolio optimization that utilizes a unique combination of synthetic data generation and a CVaR-constraint. We formulate the portfolio optimization problem as an asset allocation problem in which each asset class is accessed through a passive (index) fund. The asset-class weights are determined by solving an optimization problem which includes a CVaR-constraint. The optimization is carried out by means of a Modified CTGAN algorithm which incorporates features (contextual information) and is used to generate synthetic return scenarios, which, in turn, are fed into the optimization engine. For contextual information we rely on several points along the U.S. Treasury yield curve. The merits of this approach are demonstrated with an example based on ten asset classes (covering stocks, bonds, and commodities) over a fourteen-and-half year period (January 2008-June 2022). We also show that the synthetic generation process is able to capture well the key characteristics of the original data, and the optimization scheme results in portfolios that exhibit satisfactory out-of-sample performance. We also show that this approach outperforms the conventional equal-weights (1/N) asset allocation strategy and other optimization formulations based on historical data only.

The rapid development of social robots has challenged robotics and cognitive sciences to understand humans' perception of the appearance of robots. In this study, robot-associated words spontaneously generated by humans were analyzed to semantically reveal the body image of 30 robots that have been developed over the past decades. The analyses took advantage of word affect scales and embedding vectors, and provided a series of evidence for links between human perception and body image. It was found that the valence and dominance of the body image reflected humans' attitude towards the general concept of robots; that the user bases and usages of the robots were among the primary factors influencing humans' impressions towards individual robots; and that there was a relationship between the robots' affects and semantic distances to the word ``person''. According to the results, building body image for robots was an effective paradigm to investigate which features were appreciated by people and what influenced people's feelings towards robots.

ASR (automatic speech recognition) systems like Siri, Alexa, Google Voice or Cortana has become quite popular recently. One of the key techniques enabling the practical use of such systems in people's daily life is deep learning. Though deep learning in computer vision is known to be vulnerable to adversarial perturbations, little is known whether such perturbations are still valid on the practical speech recognition. In this paper, we not only demonstrate such attacks can happen in reality, but also show that the attacks can be systematically conducted. To minimize users' attention, we choose to embed the voice commands into a song, called CommandSong. In this way, the song carrying the command can spread through radio, TV or even any media player installed in the portable devices like smartphones, potentially impacting millions of users in long distance. In particular, we overcome two major challenges: minimizing the revision of a song in the process of embedding commands, and letting the CommandSong spread through the air without losing the voice "command". Our evaluation demonstrates that we can craft random songs to "carry" any commands and the modify is extremely difficult to be noticed. Specially, the physical attack that we play the CommandSongs over the air and record them can success with 94 percentage.