Social survey datasets, for example, are typically mixed because they include variables like age (continuous), demographic group (categorical), and Likert scales (ordinal) measuring how strongly a respondent agrees with certain stated opinions. Continuous variables are encoded as real numbers and sometimes called numeric. We refer to variables that admit a total order (e.g.

Most of the literature on matrix sensing is based on some form of explicit regularization or rank constraint to encourage or enforce low-rankness of the estimated matrix. A popular approach is based onminimizing thenuclear norm oronusing explicit regularization techniques based onthe nuclear norm, e.g.

We provide theoretical analysis on the convergence of Flow and empirically demonstrate the superiority of Flow in improving clients' accuracy compared

We present a case study on malware detection--a binary classification problem on byte sequences where classifier evasion is a well-established threat model.

The lower bound on opt( U) given in Lemma B.10 holds for ρ -metric spaces with no modifications. By making the appropriate modifications to the proof of Theorem C.1, we can extend this theorem to In particular, we can obtain a proof of Theorem A.5 by taking the proof of Theorem C.1 and adding extra ρ factors whenever the triangle inequality is applied. We first prove Lemma B.1, which shows that the sizes of the sets U By Lemma B.2, we get that Henceforth, we fix some positive ξ and sufficiently large α such that Lemma B.3 holds. By now applying Lemma B.4 it follows that The following lemma is proven in [25]. Lemma B.1, the third inequality follows from Lemma B.7, and the fourth inequality follows from the The second inequality follows from Lemma B.8, the third inequality from averaging and the choice Proof of Lemma 3.3: It follows that with probability at least 1 e Hence, by Theorem D.1, we must have that O (poly( k)) query time must have Ω( k) amortized update time.

Clustering is a fundamental problem in unsupervised learning with several practical applications. In clustering, one is interested in partitioning elements into different groups (i.e.