Karsten Borgwardt (born 1980) is a German computer scientist and biologist specializing in machine learning and computational biology. Since February 2023, he has been a director at the Max Planck Institute of Biochemistry in Martinsried, Germany, where he leads the Department of Machine Learning and Systems Biology. == Education and career == Borgwardt was born in Kaiserslautern. He obtained a Diplom (equivalent to a master’s degree) in computer science from LMU Munich in 2004 and a Master of Science in biology from the University of Oxford in 2003. In 2007, he obtained his PhD from LMU Munich in computer science. Following a postdoctoral position at the University of Cambridge, he became a research group leader for machine learning and computational biology at the Max Planck Institute for Biological Cybernetics and the former Max Planck Institute for Developmental Biology in Tübingen in 2008. In 2011, Borgwardt was appointed professor of data mining in the life sciences at the University of Tübingen. In 2014, he joined ETH Zurich as an associate professor in the Department of Biosystems Science and Engineering (D-BSSE) and was promoted to full professor in 2017. During his tenure at ETH Zurich, he coordinated significant research programs, including two Marie Curie Innovative Training Networks and the Personalized Swiss Sepsis Study, focusing on the prediction of sepsis using machine learning. In 2023, he was appointed as Scientific Member of the Max Planck Society and as Director at the Max Planck Institute of Biochemistry in Martinsried. == Research contributions == Borgwardt’s research integrates big data analysis with biomedical research. He develops novel machine learning algorithms to detect patterns and statistical dependencies in large biological and medical datasets. His work aims to enable the automatic generation of new knowledge from big data and to understand the relationship between the function of biological systems and their molecular properties, which is fundamental for personalized medicine. == Awards and honors == During his studies, he was a scholar of the Stiftung Maximilianeum, and the Bavarian Foundation for the Promotion of the Gifted. Borgwardt received scholarships from the Studienstiftung des deutschen Volkes in 2002 and 2007. His PhD dissertation received the Heinz Schwärtzel Dissertation Award for Foundations of Computer Science in 2007. As a professor in Tübingen, he was awarded the Alfried-Krupp-Förderpreis for Young Professors in 2013. In 2015, he received an SNSF Starting Grant. In 2014, 2015 and 2016, he was listed in “Top 40 under 40” in Germany rankings selected by Capital magazine. In 2018, Borgwardt was named among “25 individuals who have the potential to shape the next 25 years” by Focus magazine. In 2023, Borgwardt received an honorary professorship from LMU Munich by the Faculty of Chemistry and Pharmacy. Publications from Borgwardt's group have received the Outstanding Student Paper Award in NIPS in 2009, the SIB Graduate Paper Award in 2020 and SIB Remarkable Output Awards in 2020 and 2021 from the Swiss Institute of Bioinformatics (SIB). == Selected publications == Weisfeiler-Lehman Graph Kernels (’‘Journal of Machine Learning Research’’, 2011): Introduced an efficient graph kernel based on the Weisfeiler-Lehman algorithm. “Direct antimicrobial resistance prediction from clinical MALDI-TOF mass spectra using machine learning” (’‘Nature Medicine’’, 2022): showcased the feasibility of predicting antimicrobial resistance from readily collected mass spectrometry data in the hospital. The new method is able to identify antibiotic resistance 24 hours earlier than previous methods.
Matrix regularization
In the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the more common vector framework, Tikhonov regularization optimizes over min x ‖ A x − y ‖ 2 + λ ‖ x ‖ 2 {\displaystyle \min _{x}\left\|Ax-y\right\|^{2}+\lambda \left\|x\right\|^{2}} to find a vector x {\displaystyle x} that is a stable solution to the regression problem. When the system is described by a matrix rather than a vector, this problem can be written as min X ‖ A X − Y ‖ 2 + λ ‖ X ‖ 2 , {\displaystyle \min _{X}\left\|AX-Y\right\|^{2}+\lambda \left\|X\right\|^{2},} where the vector norm enforcing a regularization penalty on x {\displaystyle x} has been extended to a matrix norm on X {\displaystyle X} . Matrix regularization has applications in matrix completion, multivariate regression, and multi-task learning. Ideas of feature and group selection can also be extended to matrices, and these can be generalized to the nonparametric case of multiple kernel learning. == Basic definition == Consider a matrix W {\displaystyle W} to be learned from a set of examples, S = ( X i t , y i t ) {\displaystyle S=(X_{i}^{t},y_{i}^{t})} , where i {\displaystyle i} goes from 1 {\displaystyle 1} to n {\displaystyle n} , and t {\displaystyle t} goes from 1 {\displaystyle 1} to T {\displaystyle T} . Let each input matrix X i {\displaystyle X_{i}} be ∈ R D T {\displaystyle \in \mathbb {R} ^{DT}} , and let W {\displaystyle W} be of size D × T {\displaystyle D\times T} . A general model for the output y {\displaystyle y} can be posed as y i t = ⟨ W , X i t ⟩ F , {\displaystyle y_{i}^{t}=\left\langle W,X_{i}^{t}\right\rangle _{F},} where the inner product is the Frobenius inner product. For different applications the matrices X i {\displaystyle X_{i}} will have different forms, but for each of these the optimization problem to infer W {\displaystyle W} can be written as min W ∈ H E ( W ) + R ( W ) , {\displaystyle \min _{W\in {\mathcal {H}}}E(W)+R(W),} where E {\displaystyle E} defines the empirical error for a given W {\displaystyle W} , and R ( W ) {\displaystyle R(W)} is a matrix regularization penalty. The function R ( W ) {\displaystyle R(W)} is typically chosen to be convex and is often selected to enforce sparsity (using ℓ 1 {\displaystyle \ell ^{1}} -norms) and/or smoothness (using ℓ 2 {\displaystyle \ell ^{2}} -norms). Finally, W {\displaystyle W} is in the space of matrices H {\displaystyle {\mathcal {H}}} with Frobenius inner product ⟨ … ⟩ F {\displaystyle \langle \dots \rangle _{F}} . == General applications == === Matrix completion === In the problem of matrix completion, the matrix X i t {\displaystyle X_{i}^{t}} takes the form X i t = e t ⊗ e i ′ , {\displaystyle X_{i}^{t}=e_{t}\otimes e_{i}',} where ( e t ) t {\displaystyle (e_{t})_{t}} and ( e i ′ ) i {\displaystyle (e_{i}')_{i}} are the canonical basis in R T {\displaystyle \mathbb {R} ^{T}} and R D {\displaystyle \mathbb {R} ^{D}} . In this case the role of the Frobenius inner product is to select individual elements w i t {\displaystyle w_{i}^{t}} from the matrix W {\displaystyle W} . Thus, the output y {\displaystyle y} is a sampling of entries from the matrix W {\displaystyle W} . The problem of reconstructing W {\displaystyle W} from a small set of sampled entries is possible only under certain restrictions on the matrix, and these restrictions can be enforced by a regularization function. For example, it might be assumed that W {\displaystyle W} is low-rank, in which case the regularization penalty can take the form of a nuclear norm. R ( W ) = λ ‖ W ‖ ∗ = λ ∑ i | σ i | , {\displaystyle R(W)=\lambda \left\|W\right\|_{}=\lambda \sum _{i}\left|\sigma _{i}\right|,} where σ i {\displaystyle \sigma _{i}} , with i {\displaystyle i} from 1 {\displaystyle 1} to min D , T {\displaystyle \min D,T} , are the singular values of W {\displaystyle W} . === Multivariate regression === Models used in multivariate regression are parameterized by a matrix of coefficients. In the Frobenius inner product above, each matrix X {\displaystyle X} is X i t = e t ⊗ x i {\displaystyle X_{i}^{t}=e_{t}\otimes x_{i}} such that the output of the inner product is the dot product of one row of the input with one column of the coefficient matrix. The familiar form of such models is Y = X W + b {\displaystyle Y=XW+b} Many of the vector norms used in single variable regression can be extended to the multivariate case. One example is the squared Frobenius norm, which can be viewed as an ℓ 2 {\displaystyle \ell ^{2}} -norm acting either entrywise, or on the singular values of the matrix: R ( W ) = λ ‖ W ‖ F 2 = λ ∑ i ∑ j | w i j | 2 = λ Tr ( W ∗ W ) = λ ∑ i σ i 2 . {\displaystyle R(W)=\lambda \left\|W\right\|_{F}^{2}=\lambda \sum _{i}\sum _{j}\left|w_{ij}\right|^{2}=\lambda \operatorname {Tr} \left(W^{}W\right)=\lambda \sum _{i}\sigma _{i}^{2}.} In the multivariate case the effect of regularizing with the Frobenius norm is the same as the vector case; very complex models will have larger norms, and, thus, will be penalized more. === Multi-task learning === The setup for multi-task learning is almost the same as the setup for multivariate regression. The primary difference is that the input variables are also indexed by task (columns of Y {\displaystyle Y} ). The representation with the Frobenius inner product is then X i t = e t ⊗ x i t . {\displaystyle X_{i}^{t}=e_{t}\otimes x_{i}^{t}.} The role of matrix regularization in this setting can be the same as in multivariate regression, but matrix norms can also be used to couple learning problems across tasks. In particular, note that for the optimization problem min W ‖ X W − Y ‖ 2 2 + λ ‖ W ‖ 2 2 {\displaystyle \min _{W}\left\|XW-Y\right\|_{2}^{2}+\lambda \left\|W\right\|_{2}^{2}} the solutions corresponding to each column of Y {\displaystyle Y} are decoupled. That is, the same solution can be found by solving the joint problem, or by solving an isolated regression problem for each column. The problems can be coupled by adding an additional regularization penalty on the covariance of solutions min W , Ω ‖ X W − Y ‖ 2 2 + λ 1 ‖ W ‖ 2 2 + λ 2 Tr ( W T Ω − 1 W ) {\displaystyle \min _{W,\Omega }\left\|XW-Y\right\|_{2}^{2}+\lambda _{1}\left\|W\right\|_{2}^{2}+\lambda _{2}\operatorname {Tr} \left(W^{T}\Omega ^{-1}W\right)} where Ω {\displaystyle \Omega } models the relationship between tasks. This scheme can be used to both enforce similarity of solutions across tasks, and to learn the specific structure of task similarity by alternating between optimizations of W {\displaystyle W} and Ω {\displaystyle \Omega } . When the relationship between tasks is known to lie on a graph, the Laplacian matrix of the graph can be used to couple the learning problems. == Spectral regularization == Regularization by spectral filtering has been used to find stable solutions to problems such as those discussed above by addressing ill-posed matrix inversions (see for example Filter function for Tikhonov regularization). In many cases the regularization function acts on the input (or kernel) to ensure a bounded inverse by eliminating small singular values, but it can also be useful to have spectral norms that act on the matrix that is to be learned. There are a number of matrix norms that act on the singular values of the matrix. Frequently used examples include the Schatten p-norms, with p = 1 or 2. For example, matrix regularization with a Schatten 1-norm, also called the nuclear norm, can be used to enforce sparsity in the spectrum of a matrix. This has been used in the context of matrix completion when the matrix in question is believed to have a restricted rank. In this case the optimization problem becomes: min ‖ W ‖ ∗ subject to W i , j = Y i j . {\displaystyle \min \left\|W\right\|_{}~~{\text{ subject to }}~~W_{i,j}=Y_{ij}.} Spectral Regularization is also used to enforce a reduced rank coefficient matrix in multivariate regression. In this setting, a reduced rank coefficient matrix can be found by keeping just the top n {\displaystyle n} singular values, but this can be extended to keep any reduced set of singular values and vectors. == Structured sparsity == Sparse optimization has become the focus of much research interest as a way to find solutions that depend on a small number of variables (see e.g. the Lasso method). In principle, entry-wise sparsity can be enforced by penalizing the entry-wise ℓ 0 {\displaystyle \ell ^{0}} -norm of the matrix, but the ℓ 0 {\displaystyle \ell ^{0}} -norm is not convex. In practice this can be implemented by convex relaxation to the ℓ 1 {\displaystyle \ell ^{1}} -norm. While entry-wise regularization with an ℓ 1 {\displaystyle \ell ^{1}} -norm will find solutions with a small number of nonzero elements, applying an ℓ 1 {
Glushkov's construction algorithm
In computer science theory – particularly formal language theory – Glushkov's construction algorithm, invented by Victor Mikhailovich Glushkov, transforms a given regular expression into an equivalent nondeterministic finite automaton (NFA). Thus, it forms a bridge between regular expressions and nondeterministic finite automata: two abstract representations of the same class of formal languages. A regular expression may be used to conveniently describe an advanced search pattern in a "find and replace"–like operation of a text processing utility. Glushkov's algorithm can be used to transform it into an NFA, which furthermore is small by nature, as the number of its states equals the number of symbols of the regular expression, plus one. Subsequently, the NFA can be made deterministic by the powerset construction and then be minimized to get an optimal automaton corresponding to the given regular expression. The latter format is best suited for execution on a computer. From another, more theoretical point of view, Glushkov's algorithm is a part of the proof that NFA and regular expressions both accept exactly the same languages; that is, the regular languages. The converse of Glushkov's algorithm is Kleene's algorithm, which transforms a finite automaton into a regular expression. The automaton obtained by Glushkov's construction is the same as the one obtained by Thompson's construction algorithm, once its ε-transitions are removed. Glushkov's construction algorithm is also called The algorithm of Berry-Sethi, named after Gérard Berry and Ravi Sethi who worked on this construction. == Construction == Given a regular expression e, the Glushkov Construction Algorithm creates a non-deterministic automaton that accepts the language L ( e ) {\displaystyle L(e)} accepted by e. The construction uses four steps: === Step 1 === Linearisation of the expression. Each letter of the alphabet appearing in the expression e is renamed, so that each letter occurs at most once in the new expression e ′ {\displaystyle e'} . Glushkov's construction essentially relies on the fact that e ′ {\displaystyle e'} represents a local language L ( e ′ ) {\displaystyle L(e')} . Let A be the old alphabet and let B be the new one. === Step 2a === Computation of the sets P ( e ′ ) {\displaystyle P(e')} , D ( e ′ ) {\displaystyle D(e')} , and F ( e ′ ) {\displaystyle F(e')} . The first, P ( e ′ ) {\displaystyle P(e')} , is the set of letters which occurs as first letter of a word of L ( e ′ ) {\displaystyle L(e')} . The second, D ( e ′ ) {\displaystyle D(e')} , is the set of letters that can end a word of L ( e ′ ) {\displaystyle L(e')} . The last one, F ( e ′ ) {\displaystyle F(e')} , is the set of letter pairs that can occur in words of L ( e ′ ) {\displaystyle L(e')} , i.e. it is the set of factors of length two of the words of L ( e ′ ) {\displaystyle L(e')} . Those sets are mathematically defined by P ( e ′ ) = { x ∈ B ∣ x B ∗ ∩ L ( e ′ ) ≠ ∅ } {\displaystyle P(e')=\{x\in B\mid xB^{}\cap L(e')\neq \emptyset \}} , D ( e ′ ) = { y ∈ B ∣ B ∗ y ∩ L ( e ′ ) ≠ ∅ } {\displaystyle D(e')=\{y\in B\mid B^{}y\cap L(e')\neq \emptyset \}} , F ( e ′ ) = { u ∈ B 2 ∣ B ∗ u B ∗ ∩ L ( e ′ ) ≠ ∅ } {\displaystyle F(e')=\{u\in B^{2}\mid B^{}uB^{}\cap L(e')\neq \emptyset \}} . They are computed by induction over the structure of the expression, as explained below. === Step 2b === Computation of the set Λ ( e ′ ) {\displaystyle \Lambda (e')} which contains the empty word ε {\displaystyle \varepsilon } if this word belongs to L ( e ′ ) {\displaystyle L(e')} , and is the empty set otherwise. Formally, this is Λ ( e ′ ) = { ε } ∩ L ( e ′ ) {\displaystyle \Lambda (e')=\{\varepsilon \}\cap L(e')} . === Step 3 === Computation of automaton recognizing the local language, as defined by P ( e ′ ) {\displaystyle P(e')} , D ( e ′ ) {\displaystyle D(e')} , F ( e ′ ) {\displaystyle F(e')} , and Λ ( e ′ ) {\displaystyle \Lambda (e')} . By definition, the local language defined by the sets P, D, and F is the set of words which begin with a letter of P, end by a letter of D, and whose factors of length 2 belong to F, optionally also including the empty word; that is, it is the language: L ′ = ( P B ∗ ∩ B ∗ D ) ∖ B ∗ ( B 2 ∖ F ) B ∗ ∪ Λ ( e ′ ) {\displaystyle L'=(PB^{}\cap B^{}D)\setminus B^{}(B^{2}\setminus F)B^{}\cup \Lambda (e')} . Strictly speaking, it is the computation of the automaton for the local language denoted by this linearised expression that is Glushkov's construction. === Step 4 === Remove the linearisation, replacing each indexed letter B by the original letter of A. == Example == Consider the regular expression e = ( a ( a b ) ∗ ) ∗ + ( b a ) ∗ {\displaystyle e=(a(ab)^{})^{}+(ba)^{}} . == Computation of the set of letters == The computation of the sets P, D, F, and Λ is done inductively over the regular expression e ′ {\displaystyle e'} . One must give the values for ∅, ε (the symbols for the empty language and the singleton language containing the empty word), the letters, and the results of the operations + , ⋅ , ∗ {\displaystyle +,\cdot ,^{}} . The most costly operations are the cartesian products of sets for the computation of F. == Properties == The obtained automaton is non-deterministic, and it has as many states as the number of letters of the regular expression, plus one. It has been proven that every Thompson's automaton can be transformed into Glushkov's automaton via a ε-transitions elimination method. == Applications and deterministic expressions == The computation of the automaton by the expression occurs often; it has been systematically used in search functions, in particular by the Unix grep command. Similarly, XML's specification also uses such constructions; for more efficiency, regular expressions of a certain kind, called deterministic expressions, have been studied.
The Best Free AI Background Remover for Beginners
In search of the best AI background remover? An AI background remover is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI background remover slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
AI Writing Assistants: Free vs Paid (2026)
Curious about the best AI writing assistant? An AI writing assistant is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI writing assistant slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
Agent-assisted automation
Agent-assisted automation is a type of call center technology that automates elements of what the call center agent 1) does with his/her desktop tools and/or 2) says to customers during the call using pre-recorded audio. It is a relatively new category of call center technology that shows promise in improving call center productivity and compliance. == Types of agent-assisted automation == === Pre-recorded audio === Pre-recorded audio (sometimes referred to as soundboard (computer program) or as soundboard technology) is another form of agent-assisted automation. The purpose of using pre-recorded messages is to increase the probability (and in some cases error-proof the process so) that the right information is provided to customers at the right time. The required disclosures are pre-recorded to ensure accuracy and understandability. By integrating the recordings with the customer relationship management software, the right combination of disclosures can be played based on the combination of goods and services the customer purchased. The integration with the customer relationship management software also ensures that the order cannot be submitted until the disclosures are played, essentially error-proofing (poka-yoke) the process of ensuring the customer gets all the required consumer protection information. Phone surveys are ideal applications of this technology. Whether surveying market preferences or political views, the pre-recorded audio with an agent listening allows the questions to be asked in the same way every time, uninfluenced by the agents' fatigue levels, accents, or their own views. === Fraud prevention === Fraud prevention is a specialized type of agent-assisted automation focused on reducing ID theft and credit card fraud. ID theft and credit card fraud are huge threats for call centers and their customers and few good solutions exist, but new agent-assisted automation solutions are producing promising results. The technology allows the agents to remain on the phone while the customers use their phone key pads to enter the information. The tones are masked and the information passes directly into the customer relationship management system or payment gateway in the case of credit card transactions. The automation essentially makes it impossible for call center agents and also call center personnel that might be monitoring the calls to steal the credit card number, social security number, or other personally identifiable information. === Outbound telemarketing === Another specialized application space of agent-assisted automation is in outbound telemarketing, which goes under numerous headings including outbound prospecting, cold calling, solicitation, fund-raising, etc. Turnover is high among agents engaged in this kind of work because the task is tedious and emotionally difficult. It is tedious because the agent spends the bulk of their day, not talking to qualified leads, but in getting wrong numbers and answering machines. == Benefits == Just as automation has benefited manufacturing by reducing the mental and physical effort required of workers while simultaneously improving throughput, quality, and safety, agent-assisted automation is improving call center results while reducing the tiring aspects of the job for agents. In some cases, the agent-assisted automation streamlines the process and allows calls to be handled more quickly. By eliminating cutting and pasting from one application to another, by auto-navigating applications, and by providing a single view of the customer, agent-assisted automation can reduce call handle time and increase agent productivity. Second, in theory, the more steps that can be automated and the more logic that can be built into the call flow (e.g., if the customer buys items 2 and 9, then disclosures a, c, and f are read by the pre-recorded audio), then companies may be able to reduce the amount of training that is required of the agents while at the same time ensuring more consistency and accuracy. However, no published studies have reported this result yet. But an even larger problem in call centers is between-agent variation in behavior and results. Agents differ in the amount of training and coaching they receive, they differ in the amount of experience they have, their jobs are repetitious and tiring, and the process and procedures the agents are supposed to follow constantly change. Moreover, there are significant individual differences between agents in their intelligence, personality, motivations, etc. which all affect performance. Despite the large amount of money call centers have spent over decades trying to reduce between-agent variation, the problem is still so prevalent that one large study of customer interactions with call centers found that a customer's experience was completely a function of the quality of the agent who happened to answer the phone. Therefore, the most significant benefit of agent-assisted automation may prove to be in how the automation error-proofs or poka-yoke the process and ensures that something that needs to be done or said happens every time. Properly implemented, the between-agent variation for whatever step of the process the automation is applied to may be able to be reduced to near zero. This is especially important in a collection agency whose processes and procedures are closely regulated by the Fair Debt Collection Practices Act.
Is an AI Essay Writer Worth It in 2026?
Comparing the best AI essay writer? An AI essay writer is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI essay writer slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.