Koh Takeuchi

Ryosuke Ueda, Koh Takeuchi, Hisashi Kashima

Crowdsourcing has been widely used to efficiently obtain labeled datasets for supervised learning from large numbers of human resources at low cost. However, one of the technical challenges in obtaining high-quality results from crowdsourcing is dealing with the variability and bias caused by the fact that it is humans execute the work, and various studies have addressed this issue to improve the quality by integrating redundantly collected responses. In this study, we focus on the observation bias in crowdsourcing. Variations in the frequency of worker responses and the complexity of tasks occur, which may affect the aggregation results when they are correlated with the quality of the responses. We also propose statistical aggregation methods for crowdsourcing responses that are combined with an observational data bias removal method used in causal inference. Through experiments using both synthetic and real datasets with/without artificially injected spam and colluding workers, we verify that the proposed method improves the aggregation accuracy in the presence of strong observation biases and robustness to both spam and colluding workers.

Ryosuke Ueda, Koh Takeuchi, Hisashi Kashima

The aggregation of multiple opinions plays a crucial role in decision-making, such as in hiring and loan review, and in labeling data for supervised learning. Although majority voting and existing opinion aggregation models are effective for simple tasks, they are inappropriate for tasks without objectively true labels in which disagreements may occur. In particular, when voter attributes such as gender or race introduce bias into opinions, the aggregation results may vary depending on the composition of voter attributes. A balanced group of voters is desirable for fair aggregation results but may be difficult to prepare. In this study, we consider methods to achieve fair opinion aggregation based on voter attributes and evaluate the fairness of the aggregated results. To this end, we consider an approach that combines opinion aggregation models such as majority voting and the Dawid and Skene model (D&S model) with fairness options such as sample weighting. To evaluate the fairness of opinion aggregation, probabilistic soft labels are preferred over discrete class labels. First, we address the problem of soft label estimation without considering voter attributes and identify some issues with the D&S model. To address these limitations, we propose a new Soft D&S model with improved accuracy in estimating soft labels. Moreover, we evaluated the fairness of an opinion aggregation model, including Soft D&S, in combination with different fairness options using synthetic and semi-synthetic data. The experimental results suggest that the combination of Soft D&S and data splitting as a fairness option is effective for dense data, whereas weighted majority voting is effective for sparse data. These findings should prove particularly valuable in supporting decision-making by human and machine-learning models with balanced opinion aggregation.

Xiaotian Lu, Jiyi Li, Koh Takeuchi et al.

Crowdsourcing has been used to collect data at scale in numerous fields. Triplet similarity comparison is a type of crowdsourcing task, in which crowd workers are asked the question ``among three given objects, which two are more similar?'', which is relatively easy for humans to answer. However, the comparison can be sometimes based on multiple views, i.e., different independent attributes such as color and shape. Each view may lead to different results for the same three objects. Although an algorithm was proposed in prior work to produce multiview embeddings, it involves at least two problems: (1) the existing algorithm cannot independently predict multiview embeddings for a new sample, and (2) different people may prefer different views. In this study, we propose an end-to-end inductive deep learning framework to solve the multiview representation learning problem. The results show that our proposed method can obtain multiview embeddings of any object, in which each view corresponds to an independent attribute of the object. We collected two datasets from a crowdsourcing platform to experimentally investigate the performance of our proposed approach compared to conventional baseline methods.

Keisuke Fujii, Koh Takeuchi, Atsushi Kuribayashi et al.

Evaluation of intervention in a multiagent system, e.g., when humans should intervene in autonomous driving systems and when a player should pass to teammates for a good shot, is challenging in various engineering and scientific fields. Estimating the individual treatment effect (ITE) using counterfactual long-term prediction is practical to evaluate such interventions. However, most of the conventional frameworks did not consider the time-varying complex structure of multiagent relationships and covariate counterfactual prediction. This may lead to erroneous assessments of ITE and difficulty in interpretation. Here we propose an interpretable, counterfactual recurrent network in multiagent systems to estimate the effect of the intervention. Our model leverages graph variational recurrent neural networks and theory-based computation with domain knowledge for the ITE estimation framework based on long-term prediction of multiagent covariates and outcomes, which can confirm the circumstances under which the intervention is effective. On simulated models of an automated vehicle and biological agents with time-varying confounders, we show that our methods achieved lower estimation errors in counterfactual covariates and the most effective treatment timing than the baselines. Furthermore, using real basketball data, our methods performed realistic counterfactual predictions and evaluated the counterfactual passes in shot scenarios.

Shunki Uebayashi, Kento Masui, Kyohei Atarashi et al.

Multimodal Large Language Models (MLLMs) have recently emerged as general architectures capable of reasoning over diverse modalities. Benchmarks for MLLMs should measure their ability for cross-modal integration. However, current benchmarks are filled with shortcut questions, which can be solved using only a single modality, thereby yielding unreliable rankings. For example, in vision-language cases, we can find the correct answer without either the image or the text. These low-quality questions unnecessarily increase the size and computational requirements of benchmarks. We introduce a multi-modal and multidimensional item response theory framework (M3IRT) that extends classical IRT by decomposing both model ability and item difficulty into image-only, text-only, and cross-modal components. M3IRT estimates cross-modal ability of MLLMs and each question's cross-modal difficulty, enabling compact, high-quality subsets that better reflect multimodal reasoning. Across 24 VLMs on three benchmarks, M3IRT prioritizes genuinely cross-modal questions over shortcuts and preserves ranking fidelity even when 50% of items are artificially generated low-quality questions, thereby reducing evaluation cost while improving reliability. M3IRT thus offers a practical tool for assessing cross-modal reasoning and refining multimodal benchmarks.

Clémence Réda, Tomas Rigaux, Hiba Bederina et al.

A core research question in recommender systems is to propose batches of highly relevant and diverse items, that is, items personalized to the user's preferences, but which also might get the user out of their comfort zone. This diversity might induce properties of serendipidity and novelty which might increase user engagement or revenue. However, many real-life problems arise in that case: e.g., avoiding to recommend distinct but too similar items to reduce the churn risk, and computational cost for large item libraries, up to millions of items. First, we consider the case when the user feedback model is perfectly observed and known in advance, and introduce an efficient algorithm called B-DivRec combining determinantal point processes and a fuzzy denuding procedure to adjust the degree of item diversity. This helps enforcing a quality-diversity trade-off throughout the user history. Second, we propose an approach to adaptively tailor the quality-diversity trade-off to the user, so that diversity in recommendations can be enhanced if it leads to positive feedback, and vice-versa. Finally, we illustrate the performance and versatility of B-DivRec in the two settings on synthetic and real-life data sets on movie recommendation and drug repurposing.

Xiaofeng Lin, Guoxi Zhang, Xiaotian Lu et al.

Treatment effect estimation can assist in effective decision-making in e-commerce, medicine, and education. One popular application of this estimation lies in the prediction of the impact of a treatment (e.g., a promotion) on an outcome (e.g., sales) of a particular unit (e.g., an item), known as the individual treatment effect (ITE). In many online applications, the outcome of a unit can be affected by the treatments of other units, as units are often associated, which is referred to as interference. For example, on an online shopping website, sales of an item will be influenced by an advertisement of its co-purchased item. Prior studies have attempted to model interference to estimate the ITE accurately, but they often assume a homogeneous interference, i.e., relationships between units only have a single view. However, in real-world applications, interference may be heterogeneous, with multi-view relationships. For instance, the sale of an item is usually affected by the treatment of its co-purchased and co-viewed items. We hypothesize that ITE estimation will be inaccurate if this heterogeneous interference is not properly modeled. Therefore, we propose a novel approach to model heterogeneous interference by developing a new architecture to aggregate information from diverse neighbors. Our proposed method contains graph neural networks that aggregate same-view information, a mechanism that aggregates information from different views, and attention mechanisms. In our experiments on multiple datasets with heterogeneous interference, the proposed method significantly outperforms existing methods for ITE estimation, confirming the importance of modeling heterogeneous interference.

Xiaotian Lu, Jiyi Li, Zhen Wan et al.

Deep learning models have performed well on many NLP tasks. However, their internal mechanisms are typically difficult for humans to understand. The development of methods to explain models has become a key issue in the reliability of deep learning models in many important applications. Various saliency explanation methods, which give each feature of input a score proportional to the contribution of output, have been proposed to determine the part of the input which a model values most. Despite a considerable body of work on the evaluation of saliency methods, whether the results of various evaluation metrics agree with human cognition remains an open question. In this study, we propose a new human-based method to evaluate saliency methods in NLP by crowdsourcing. We recruited 800 crowd workers and empirically evaluated seven saliency methods on two datasets with the proposed method. We analyzed the performance of saliency methods, compared our results with existing automated evaluation methods, and identified notable differences between NLP and computer vision (CV) fields when using saliency methods. The instance-level data of our crowdsourced experiments and the code to reproduce the explanations are available at https://github.com/xtlu/lreccoling_evaluation.

Yuma Aoki, Joon Park, Koh Takeuchi et al.

This study addresses an important gap in time series outlier detection by proposing a novel problem setting: long-term outlier prediction. Conventional methods primarily focus on immediate detection by identifying deviations from normal patterns. As a result, their applicability is limited when forecasting outlier events far into the future. To overcome this limitation, we propose a simple and unsupervised two-layer method that is independent of specific models. The first layer performs standard outlier detection, and the second layer predicts future outlier scores based on the temporal structure of previously observed outliers. This framework enables not only pointwise detection but also long-term forecasting of outlier likelihoods. Experiments on synthetic datasets show that the proposed method performs well in both detection and prediction tasks. These findings suggest that the method can serve as a strong baseline for future work in outlier detection and forecasting.

Yasuaki Sumita, Koh Takeuchi, Hisashi Kashima

Large Language Models (LLMs) are trained on large corpora written by humans and demonstrate high performance on various tasks. However, as humans are susceptible to cognitive biases, which can result in irrational judgments, LLMs can also be influenced by these biases, leading to irrational decision-making. For example, changing the order of options in multiple-choice questions affects the performance of LLMs due to order bias. In our research, we first conducted an extensive survey of existing studies examining LLMs' cognitive biases and their mitigation. The mitigation techniques in LLMs have the disadvantage that they are limited in the type of biases they can apply or require lengthy inputs or outputs. We then examined the effectiveness of two mitigation methods for humans, SoPro and AwaRe, when applied to LLMs, inspired by studies in crowdsourcing. To test the effectiveness of these methods, we conducted experiments on GPT-3.5 and GPT-4 to evaluate the influence of six biases on the outputs before and after applying these methods. The results demonstrate that while SoPro has little effect, AwaRe enables LLMs to mitigate the effect of these biases and make more rational responses.

Joon Park, Kyohei Atarashi, Koh Takeuchi et al.

This paper addresses the challenge of comprehending very long contexts in Large Language Models (LLMs) by proposing a method that emulates Retrieval Augmented Generation (RAG) through specialized prompt engineering and chain-of-thought (CoT) reasoning. While recent LLMs support over 100,000 tokens in a single prompt, simply enlarging context windows has not guaranteed robust multi-hop reasoning when key details are scattered across massive input. Our approach treats the model as both the retriever and the reasoner: it first tags relevant segments within a long passage, then employs a stepwise CoT workflow to integrate these pieces of evidence. This single-pass method thereby reduces reliance on an external retriever, yet maintains focus on crucial segments. We evaluate our approach on selected tasks from BABILong, which interleaves standard bAbI QA problems with large amounts of distractor text. Compared to baseline (no retrieval) and naive RAG pipelines, our approach more accurately handles multi-fact questions such as object location tracking, counting, and indefinite knowledge. Furthermore, we analyze how prompt structure, including the order of question, relevant-text tags, and overall instructions, significantly affects performance. These findings underscore that optimized prompt engineering, combined with guided reasoning, can enhance LLMs' long-context comprehension and serve as a lightweight alternative to traditional retrieval pipelines.

Katsumi Takahashi, Koh Takeuchi, Hisashi Kashima

Machine learning models usually assume that a set of feature values used to obtain an output is fixed in advance. However, in many real-world problems, a cost is associated with measuring these features. To address the issue of reducing measurement costs, various methods have been proposed to dynamically select which features to measure, but existing methods assume that the set of measurable features remains constant, which makes them unsuitable for cases where the set of measurable features varies from instance to instance. To overcome this limitation, we define a new problem setting for Dynamic Feature Selection (DFS) with variable feature sets and propose a deep learning method that utilizes prior information about each feature, referred to as ''features of features''. Experimental results on several datasets demonstrate that the proposed method effectively selects features based on the prior information, even when the set of measurable features changes from instance to instance.

Xiaoyang Xu, Xiaofeng Lin, Koh Takeuchi et al.

Anomaly detection in dynamic graphs is a critical task with broad real-world applications, including social networks, e-commerce, and cybersecurity. Most existing methods assume that normal patterns remain stable over time; however, this assumption often fails in practice due to the phenomenon we refer to as normality distribution shift (NDS), where normal behaviors evolve over time. Ignoring NDS can lead models to misclassify shifted normal instances as anomalies, degrading detection performance. To tackle this issue, we propose WhENDS, a novel unsupervised anomaly detection method that aligns normal edge embeddings across time by estimating distributional statistics and applying whitening transformations. Extensive experiments on four widely-used dynamic graph datasets show that WhENDS consistently outperforms nine strong baselines, achieving state-of-the-art results and underscoring the importance of addressing NDS in dynamic graph anomaly detection.

Lijia Liu, Takumi Kondo, Kyohei Atarashi et al.

This paper investigates defenses for LLM-based evaluation systems against prompt injection. We formalize a class of threats called blind attacks, where a candidate answer is crafted independently of the true answer to deceive the evaluator. To counter such attacks, we propose a framework that augments Standard Evaluation (SE) with Counterfactual Evaluation (CFE), which re-evaluates the submission against a deliberately false ground-truth answer. An attack is detected if the system validates an answer under both standard and counterfactual conditions. Experiments show that while standard evaluation is highly vulnerable, our SE+CFE framework significantly improves security by boosting attack detection with minimal performance trade-offs.

Yaqi Sun, Kyohei Atarashi, Koh Takeuchi et al.

Large Vision-Language Models (LVLMs) integrate image encoders with Large Language Models (LLMs) to process multi-modal inputs and perform complex visual tasks. However, they often generate hallucinations by describing non-existent objects or attributes, compromising their reliability. This study analyzes hallucination patterns in image captioning, showing that not all tokens in the generation process are influenced by image input and that image dependency can serve as a useful signal for hallucination detection. To address this, we develop an automated pipeline to identify hallucinated objects and train a token-level classifier using hidden representations from parallel inference passes-with and without image input. Leveraging this classifier, we introduce a decoding strategy that effectively controls hallucination rates in image captioning at inference time.

Ryota Maruo, Koh Takeuchi, Hisashi Kashima

Designing two-sided matching mechanisms is challenging when practical demands for matching outcomes are difficult to formalize and the designed mechanism must satisfy theoretical conditions. To address this, prior work has proposed a framework that learns a matching mechanism from examples, using a parameterized family that satisfies properties such as stability. However, despite its usefulness, this framework does not guarantee strategy-proofness (SP), and cannot handle varying numbers of agents or incorporate publicly available contextual information about agents, both of which are crucial in real-world applications. In this paper, we propose a new parametrized family of matching mechanisms that always satisfy strategy-proofness, are applicable for an arbitrary number of agents, and deal with public contextual information of agents, based on the serial dictatorship (SD). This family is represented by NeuralSD, a novel neural network architecture based on SD, where agent rankings in SD are treated as learnable parameters computed from agents' contexts using an attention-based sub-network. To enable learning, we introduce tensor serial dictatorship (TSD), a differentiable relaxation of SD using tensor operations. This allows NeuralSD to be trained end-to-end from example matchings while satisfying SP. We conducted experiments to learn a matching mechanism from matching examples while satisfying SP. We demonstrated that our method outperformed baselines in predicting matchings and on several metrics for goodness of matching outcomes.

Ryota Maruo, Koh Takeuchi, Hisashi Kashima

The fair allocation of indivisible resources is a fundamental problem. Existing research has developed various allocation mechanisms or algorithms to satisfy different fairness notions. For example, round robin (RR) was proposed to meet the fairness criterion known as envy-freeness up to one good (EF1). Expert algorithms without mathematical formulations are used in real-world resource allocation problems to find preferable outcomes for users. Therefore, we aim to design mechanisms that strictly satisfy good properties with replicating expert knowledge. However, this problem is challenging because such heuristic rules are often difficult to formalize mathematically, complicating their integration into theoretical frameworks. Additionally, formal algorithms struggle to find preferable outcomes, and directly replicating these implicit rules can result in unfair allocations because human decision-making can introduce biases. In this paper, we aim to learn implicit allocation mechanisms from examples while strictly satisfying fairness constraints, specifically focusing on learning EF1 allocation mechanisms through supervised learning on examples of reported valuations and corresponding allocation outcomes produced by implicit rules. To address this, we developed a neural RR (NRR), a novel neural network that parameterizes RR. NRR is built from a differentiable relaxation of RR and can be trained to learn the agent ordering used for RR. We conducted experiments to learn EF1 allocation mechanisms from examples, demonstrating that our method outperforms baselines in terms of the proximity of predicted allocations and other metrics.

Sein Minn, Jill-Jenn Vie, Koh Takeuchi et al.

Intelligent Tutoring Systems have become critically important in future learning environments. Knowledge Tracing (KT) is a crucial part of that system. It is about inferring the skill mastery of students and predicting their performance to adjust the curriculum accordingly. Deep Learning-based KT models have shown significant predictive performance compared with traditional models. However, it is difficult to extract psychologically meaningful explanations from the tens of thousands of parameters in neural networks, that would relate to cognitive theory. There are several ways to achieve high accuracy in student performance prediction but diagnostic and prognostic reasoning is more critical in learning sciences. Since KT problem has few observable features (problem ID and student's correctness at each practice), we extract meaningful latent features from students' response data by using machine learning and data mining techniques. In this work, we present Interpretable Knowledge Tracing (IKT), a simple model that relies on three meaningful latent features: individual skill mastery, ability profile (learning transfer across skills), and problem difficulty. IKT's prediction of future student performance is made using a Tree-Augmented Naive Bayes Classifier (TAN), therefore its predictions are easier to explain than deep learning-based student models. IKT also shows better student performance prediction than deep learning-based student models without requiring a huge amount of parameters. We conduct ablation studies on each feature to examine their contribution to student performance prediction. Thus, IKT has great potential for providing adaptive and personalized instructions with causal reasoning in real-world educational systems.

Xiaotian Lu, Arseny Tolmachev, Tatsuya Yamamoto et al.

Understanding the reasons behind the predictions made by deep neural networks is critical for gaining human trust in many important applications, which is reflected in the increasing demand for explainability in AI (XAI) in recent years. Saliency-based feature attribution methods, which highlight important parts of images that contribute to decisions by classifiers, are often used as XAI methods, especially in the field of computer vision. In order to compare various saliency-based XAI methods quantitatively, several approaches for automated evaluation schemes have been proposed; however, there is no guarantee that such automated evaluation metrics correctly evaluate explainability, and a high rating by an automated evaluation scheme does not necessarily mean a high explainability for humans. In this study, instead of the automated evaluation, we propose a new human-based evaluation scheme using crowdsourcing to evaluate XAI methods. Our method is inspired by a human computation game, "Peek-a-boom", and can efficiently compare different XAI methods by exploiting the power of crowds. We evaluate the saliency maps of various XAI methods on two datasets with automated and crowd-based evaluation schemes. Our experiments show that the result of our crowd-based evaluation scheme is different from those of automated evaluation schemes. In addition, we regard the crowd-based evaluation results as ground truths and provide a quantitative performance measure to compare different automated evaluation schemes. We also discuss the impact of crowd workers on the results and show that the varying ability of crowd workers does not significantly impact the results.

Luu Huu Phuc, Koh Takeuchi, Seiji Okajima et al.

Multi-relational graph is a ubiquitous and important data structure, allowing flexible representation of multiple types of interactions and relations between entities. Similar to other graph-structured data, link prediction is one of the most important tasks on multi-relational graphs and is often used for knowledge completion. When related graphs coexist, it is of great benefit to build a larger graph via integrating the smaller ones. The integration requires predicting hidden relational connections between entities belonged to different graphs (inter-domain link prediction). However, this poses a real challenge to existing methods that are exclusively designed for link prediction between entities of the same graph only (intra-domain link prediction). In this study, we propose a new approach to tackle the inter-domain link prediction problem by softly aligning the entity distributions between different domains with optimal transport and maximum mean discrepancy regularizers. Experiments on real-world datasets show that optimal transport regularizer is beneficial and considerably improves the performance of baseline methods.

Naoya Takeishi, Keisuke Fujii, Koh Takeuchi et al.

Extracting coherent patterns is one of the standard approaches towards understanding spatio-temporal data. Dynamic mode decomposition (DMD) is a powerful tool for extracting coherent patterns, but the original DMD and most of its variants do not consider label information, which is often available as side information of spatio-temporal data. In this work, we propose a new method for extracting distinctive coherent patterns from labeled spatio-temporal data collections, such that they contribute to major differences in a labeled set of dynamics. We achieve such pattern extraction by incorporating discriminant analysis into DMD. To this end, we define a kernel function on subspaces spanned by sets of dynamic modes and develop an objective to take both reconstruction goodness as DMD and class-separation goodness as discriminant analysis into account. We illustrate our method using a synthetic dataset and several real-world datasets. The proposed method can be a useful tool for exploratory data analysis for understanding spatio-temporal data.

Koh Takeuchi, Ryo Nishida, Hisashi Kashima et al.

Crowd movement guidance has been a fascinating problem in various fields, such as easing traffic congestion in unusual events and evacuating people from an emergency-affected area. To grab the reins of crowds, there has been considerable demand for a decision support system that can answer a typical question: ``what will be the outcomes of each of the possible options in the current situation. In this paper, we consider the problem of estimating the effects of crowd movement guidance from past data. To cope with limited amount of available data biased by past decision-makers, we leverage two recent techniques in deep representation learning for spatial data analysis and causal inference. We use a spatial convolutional operator to extract effective spatial features of crowds from a small amount of data and use balanced representation learning based on the integral probability metrics to mitigate the selection bias and missing counterfactual outcomes. To evaluate the performance on estimating the treatment effects of possible guidance, we use a multi-agent simulator to generate realistic data on evacuation scenarios in a crowded theater, since there are no available datasets recording outcomes of all possible crowd movement guidance. The results of three experiments demonstrate that our proposed method reduces the estimation error by at most 56% from state-of-the-art methods.

Shunsuke Kanda, Koh Takeuchi, Keisuke Fujii et al.

Massive datasets of spatial trajectories representing the mobility of a diversity of moving objects are ubiquitous in research and industry. Similarity search of a large collection of trajectories is indispensable for turning these datasets into knowledge. Locality sensitive hashing (LSH) is a powerful technique for fast similarity searches. Recent methods employ LSH and attempt to realize an efficient similarity search of trajectories; however, those methods are inefficient in terms of search time and memory when applied to massive datasets. To address this problem, we present the trajectory-indexing succinct trit-array trie (tSTAT), which is a scalable method leveraging LSH for trajectory similarity searches. tSTAT quickly performs the search on a tree data structure called trie. We also present two novel techniques that enable to dramatically enhance the memory efficiency of tSTAT. One is a node reduction technique that substantially omits redundant trie nodes while maintaining the time performance. The other is a space-efficient representation that leverages the idea behind succinct data structures (i.e., a compressed data structure supporting fast data operations). We experimentally test tSTAT on its ability to retrieve similar trajectories for a query from large collections of trajectories and show that tSTAT performs superiorly in comparison to state-of-the-art similarity search methods.

Akisato Kimura, Zoubin Ghahramani, Koh Takeuchi et al.

In this paper, we propose a simple but effective method for training neural networks with a limited amount of training data. Our approach inherits the idea of knowledge distillation that transfers knowledge from a deep or wide reference model to a shallow or narrow target model. The proposed method employs this idea to mimic predictions of reference estimators that are more robust against overfitting than the network we want to train. Different from almost all the previous work for knowledge distillation that requires a large amount of labeled training data, the proposed method requires only a small amount of training data. Instead, we introduce pseudo training examples that are optimized as a part of model parameters. Experimental results for several benchmark datasets demonstrate that the proposed method outperformed all the other baselines, such as naive training of the target model and standard knowledge distillation.

Makoto Yamada, Koh Takeuchi, Tomoharu Iwata et al.

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function defined by local sparse models, one at each data point. We introduce sample-wise network regularization to borrow strength across the models, and sample-wise exclusive group sparsity (a.k.a., $\ell_{1,2}$ norm) to introduce diversity into the choice of feature sets in the local models. The local models are interpretable in terms of similarity of their sparsity patterns. The cost function is convex, and thus has a globally optimal solution. Moreover, we propose a simple yet efficient iterative least-squares based optimization procedure for the localized Lasso, which does not need a tuning parameter, and is guaranteed to converge to a globally optimal solution. The solution is empirically shown to outperform alternatives for both simulated and genomic personalized medicine data.