Biomarker screening method based on derivable L-1 model

Abstract

The invention discloses a biomarker screening method based on a derivable L-1 model. The method comprises the following steps: acquiring clinical manifestation data of a detected object and a corresponding biomarker, and preprocessing the clinical manifestation data and the corresponding biomarker; according to the clinical manifestation data and the corresponding biomarkers, screening the biomarkers through an L-1 model; wherein the clinical manifestation data is set as y, the biomarkers are set as a matrix H, the screening of the biomarkers is set as a vector x, the value of an element in x is 1 or 0, 1 represents that the corresponding biomarker is valid, 0 represents that the corresponding biomarker is invalid, and the matrix H represents that the matrix H represents that the corresponding biomarker is invalid. And solving # imgabs0 # by minimizing the L-1 mode of x and the L-2 mode of y-Hx so as to complete the screening of the biomarkers.

Description

Technical Field

[0001] The present invention belongs to the technical field of biomarker screening, and in particular relates to a biomarker screening method based on a differentiable L-1 model. Background Art

[0002] In the screening of biomarkers, our goal is to find biochemical indicators that correspond to certain diseases, phenotypes or other characteristics. These biochemical indicators can play an important role in the classification, early diagnosis and prevention of diseases, drug development, and design of treatment plans. The difficulty we usually face is that we may get a large number of candidate biomarkers and some observed phenotypes, but we don’t know which specific biomarkers will cause the observed phenotypes. We need to infer the biomarkers that work through calculations, but this calculation is usually uncertain. For this reason, we need to define a suitable objective function and calculate the biomarkers that work under the premise of optimizing this objective function. This objective function generally involves the L-1 model, but the L-1 model currently used cannot be differentiated, which brings some difficulties to its use.

[0003] Specifically, in the screening of biomarkers, when studying the disease phenotypes of organisms such as humans, we hope to know which biomarkers or genes play a role in these phenotypes. The problem we usually face is that we have a large number of candidate markers, but we don’t know which specific markers play a role in the diseases or phenotypes of organisms such as humans. At the same time, the measurement of these phenotypes, that is, the observed data, is noisy, which increases the difficulty of selecting markers. Therefore, we need to use some methods to pick out the biomarkers that are most likely to play a role in a certain disease phenotype. At this time, a principle to follow is to emphasize sparsity, that is, to find a small number of biomarkers that really work, rather than assuming that all candidate markers have more or less effects. A technique used at this time is to solve a system of linear equations, and the goal of the solution process is to find a solution whose L-1 modulus is the smallest. At this time, the solution or biomarker obtained is also the most sparse.

[0004] In the prior art, the L-1 norm is usually defined as the absolute value of a variable x, i.e., |x|. The use of the L-1 norm usually requires finding its first-order derivative, but the L-1 norm in the form of |x| cannot calculate its derivative. Therefore, the existing technical solution involving the L-1 norm is to use numerical methods to gradually obtain the minimum value of a model (or a certain form of maximum value), that is, to find the extreme value of a model with an absolute value such as |x|, and then apply the obtained result to the model to achieve biomarker screening. Summary of the invention

[0005] The purpose of the embodiments of the present application is to provide a method for screening biomarkers based on a differentiable L-1 module to solve the technical problem that the L-1 module is not differentiable (not differentiable) according to its definition when used in biomarker screening.

[0006] According to a first aspect of an embodiment of the present application, a method for screening biomarkers based on a differentiable L-1 model is provided, comprising:

[0007] (1) Obtaining clinical manifestation data and corresponding biomarkers of the test subjects and performing preprocessing;

[0008] (2) Based on the clinical performance data and the corresponding biomarkers, the biomarkers are screened by L-1 modulus; wherein the clinical performance data is set as y, the biomarkers are set as matrix H, and the screening of biomarkers is set as vector x, the value of the elements in x is 1 or 0, 1 indicates that the corresponding biomarker is effective, and 0 indicates that the corresponding biomarker is invalid, and the L-1 modulus of x and the L-2 modulus of y-Hx are minimized to obtain Thus, the screening of biomarkers is completed.

[0009] Furthermore, the preprocessing in step (1) includes completing the missing data by linear or nonlinear interpolation and standardizing the data, thereby converting the data into a Gaussian distribution with a mean of zero and a variance of 1.

[0010] Furthermore, the objective function for biomarker screening is:

[0011]

[0012]

[0013] Where α is the weight coefficient, for L-1 module.

[0014] Furthermore, the objective function for biomarker screening is:

[0015]

[0016]

[0017] Where α is the weight coefficient, for L-1 module.

[0018] Further, the objective function is solved to obtain include:

[0019] (i) Select a step size parameter β and initialize a The superscript 0 indicates that the current iteration is the 0th iteration;

[0020] (ii) In the first iteration, calculate For the vector n is the number of biomarkers;

[0021] (iii) Repeat the iterations of step (ii) until is smaller than a predetermined threshold ε.

[0022] According to a second aspect of an embodiment of the present application, a screening device for biomarkers based on a differentiable L-1 model is provided, comprising:

[0023] A data acquisition module is used to acquire the clinical manifestation data and corresponding biomarkers of the test subject and perform preprocessing;

[0024] A biomarker screening module is used to screen the biomarkers through the L-1 module according to the clinical performance data and the corresponding biomarkers; wherein the clinical performance data is set as y, the biomarker is set as the matrix H, and the screening of the biomarker is set as the vector x, the value of the element in x is 1 or 0, 1 indicates that the corresponding biomarker is effective, and 0 indicates that the corresponding biomarker is invalid, and the L-1 module of x and the L-2 module of y-Hx are minimized to obtain Thus, the screening of biomarkers is completed.

[0025] According to a third aspect of an embodiment of the present application, there is provided an electronic device, including:

[0026] one or more processors;

[0027] A memory for storing one or more programs;

[0028] When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in the first aspect.

[0029] According to a fourth aspect of an embodiment of the present application, a computer-readable storage medium is provided, on which computer instructions are stored, and when the instructions are executed by a processor, the steps of the method described in the first aspect are implemented.

[0030] The technical solution provided by the embodiments of the present application may have the following beneficial effects:

[0031] The objective function of biomarker screening designed in this application is to minimize the L-1 modulus of x and the L-2 modulus of y-Hx, so that the biomarkers found are truly effective for clinical manifestations and the number of biomarkers found is as small as possible, thereby making the biomarker screening results more accurate.

[0032] In addition, the present application proposes a new L-1 module design, which allows the L-1 module to be differentiated under certain conditions, so that the model with the L-1 module can adopt many ready-made methods for finding extreme values ​​(such as iterative methods), thereby making the screening of biomarkers easier.

[0033] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0035] Figure 1 The figure is a flow chart of a method for screening biomarkers based on a differentiable L-1 model according to an exemplary embodiment.

[0036] Figure 2 is a comparison diagram of a traditional L-1 mode and the L-1 mode in the present application according to an exemplary embodiment.

[0037] Figure 3 It is a block diagram of a biomarker screening device based on a differentiable L-1 model according to an exemplary embodiment.

[0038] Figure 4 is a schematic diagram of an electronic device according to an exemplary embodiment. DETAILED DESCRIPTION

[0039] Here, exemplary embodiments are described in detail, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application.

[0040] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms of "a", "said" and "the" used in this application and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0041] It should be understood that although the terms first, second, third, etc. may be used in the present application to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0042] Figure 1 is a flow chart of a method for screening biomarkers based on a differentiable L-1 model according to an exemplary embodiment. Figure 1 As shown, the method may include the following steps:

[0043] (1) Obtaining clinical manifestation data and corresponding biomarkers of the test subjects and performing preprocessing;

[0044] Specifically, we have collected clinical data of some patients through instruments and other means, such as hypertension, diabetes, arthritis, etc. These data can be represented by a vector y, for example, patients with hypertension are represented by 1, and those without hypertension are represented by 0. At the same time, we have also received potential biomarkers that may cause these clinical manifestations, such as electrocardiograms, electroencephalograms, susceptibility genes, microRNAs, proteins, small molecule compounds, etc. These biomarkers are represented by a matrix H. Each row of H corresponds to a case of a patient or an ordinary person, and each column of H reflects the values ​​we observe on the susceptibility genes, microRNAs, and proteins of this case, such as the level of a certain protein in a certain case. In this step, we also preprocess the observed data, including filling in the missing data through linear or nonlinear interpolation, and standardizing the data, so as to transform the data into a Gaussian distribution with a mean of zero and a variance of 1.

[0045] (2) Based on the clinical performance data and the corresponding biomarkers, the biomarkers are screened by L-1 modulus; wherein the clinical performance data is set as y, the biomarkers are set as matrix H, and the screening of biomarkers is set as vector x, the value of the elements in x is 1 or 0, 1 indicates that the corresponding biomarker is effective, and 0 indicates that the corresponding biomarker is invalid, and the L-1 modulus of x and the L-2 modulus of y-Hx are minimized to obtain Thus completing the screening of biomarkers;

[0046] Specifically, in the screening of biomarkers, the observed phenotype is set as y, the collected biomarkers are set as a matrix H, and the screening of biomarkers is set as a vector x. It is hoped that the value of the elements in this vector is either 1 (indicating that the corresponding biomarker is effective) or 0 (indicating that the corresponding biomarker is invalid). The goal is to calculate x through y and H, which means that the L-1 modulus of x is as small as possible, that is, it is hoped that several biomarkers that really work can be found.

[0047] In this application, the problem to be solved is

[0048] y=Hx, (1)

[0049] We need to solve for x. Here we assume is a true solution. This application needs to find a Make The smaller the difference or distance between the observed y, the better. Make the following objective function as small as possible:

[0050]

[0051] That is, the L-2 module is as small as possible. The solution of is undetermined in most cases, that is, there can be many All of them can satisfy the condition y = Hx. Therefore, it is necessary to impose restrictions on x. In practical applications, the restrictions are that most values ​​in x are zero and a few are 1. That is, it is expected that for a clinical manifestation, the biomarkers that work should be a limited number of biomarkers, rather than all the biomarkers we can measure. So we also hope The smaller the L-1 modulus, the better. The smaller the better. Under this requirement, the objective function we actually need to solve becomes

[0052]

[0053] Where α is a constant used to control the relative importance of the two terms. It is not differentiable, and the only way to solve the above equation is by numerical method.

[0054] Therefore, this application proposes a new L-1 module design. For variable x, its L-1 module is

[0055] L(x)=e x +e -x (4)

[0056] This design removes the absolute value sign in the traditional definition and approximates the property of the L-1 modulus in the traditional definition through two exponential terms, that is, if x is positive, the larger x is, the larger its modulus is. Conversely, if x is negative, the more negative x is, the larger its modulus is.

[0057] In the above design, L(x) grows towards both sides with x=0 as the center, but its growth shape is not a straight line at a 45-degree angle, but an arc, that is, L(x) is not linear in the interval of x>0 or x<0. For this reason, the present application further designs a quasi-linear L-1 module, which is expressed as

[0058] logL(x)=log(e x +e -x ). (5)

[0059] This quasi-linear L-1 norm is basically a linear form in the interval of x>0 or x<0. Figure 2 As shown, the traditional L-1 mode |x| (dashed line) and the logL(x)=log(e x +e -x ) as the shape of the L-1 mode (solid line) with a quasi-linear first-order differentiable, it can be seen that they are very similar, especially in the intervals of x greater than 1.5 or x less than -1.5.

[0060] When using L(x) or logL(x) for calculations, in order to prevent e from appearing in the intermediate steps x or e -x If x is too large to be accepted by the computer, you can multiply x by a coefficient greater than or less than one to make e x or e -x The value of falls within the acceptable range of the computer.

[0061] For the calculation of the L-1 norm above, if the independent variable of the function is a single variable x, then L(x) = e x +e -x , and logL(x)=log(e x +e -x ); if the independent variable of the function is a set of variables, such as x=[x 1 , x 2 , x 3 ], then the above operations, including the derivative operation, become operations on each data point, that is,

[0062]

[0063] at the same time

[0064] Furthermore, the first-order derivative of L(x) is

[0065]

[0066] At the same time, the first-order derivative of logL(x) is

[0067]

[0068] When using the above designed L(x) or logL(x) as the L-1 modulus, this modulus can appear in the objective function, regularization term, and other places. The calculation of this modulus, especially the calculation of the first-order derivative, can obtain the following results. If the modulus appears in the form of L(x), its first-order derivative is e x -e -x If the modulus is in the form of logL(x), its first-order derivative is (e x -e -x ) / (e x +e -x ).

[0069] When you need to find the extreme value of a model with L(x) or logL(x), you can use their corresponding first-order derivatives to perform gradient descent or similar methods until the extreme value of the model is found or other conditions are met. This type of method can be a direct method or an iterative method. In the iterative method, the user needs to control the step size of the iteration.

[0070] In the specific solution, we use formula (5) to replace the formula (3) Thus, a new objective function is obtained as follows

[0071]

[0072] This new objective function is now differentiable, so we can use existing analytical methods to solve it. There are many existing analytical methods. For example, we can use an iterative method to solve formula (6). The following is a solution:

[0073] (i) Select a step size parameter β and initialize a Here the superscript indicates the 0th iteration.

[0074] (ii)

[0075] (iii)

[0076] (iv)…

[0077] (v) until is less than a preset threshold ε.

[0078] In the above description, for the sake of clarity, the second item in the square brackets is written as But it should be made clear that is a vector of length n such that So this is for each Operation, that is

[0079]

[0080] And so on and so forth.

[0081] like Figure 2 As shown, the traditional L-1 mode |x| (dashed line) and the logL(x)=log(e x +e -x ) as the shape of the L-1 mode (solid line) with a quasi-linear first-order differentiable, it can be seen that they are very similar, especially in the intervals of x greater than 1.5 or x less than -1.5.

[0082] It should be noted that in a specific implementation, the base of the differentiable L-1 module proposed in the present application can be replaced by other values ​​from e, such as 2, 3, 4, 5 or larger values, depending on the value range of the data x to be processed.

[0083] Corresponding to the aforementioned embodiment of a method for screening biomarkers based on a differentiable L-1 module, the present application also provides an embodiment of a device for screening biomarkers based on a differentiable L-1 module.

[0084] Figure 3 FIG. 1 is a block diagram of a biomarker screening device based on a differentiable L-1 model according to an exemplary embodiment. Figure 3 , the device may include:

[0085] A data acquisition module 21 is used to acquire the clinical manifestation data and corresponding biomarkers of the test subject and perform preprocessing;

[0086] The biomarker screening module 22 is used to screen the biomarkers through the L-1 modulus according to the clinical performance data and the corresponding biomarkers; wherein the clinical performance data is set as y, the biomarker is set as the matrix H, and the screening of the biomarkers is set as the vector x, the value of the element in x is 1 or 0, 1 indicates that the corresponding biomarker is valid, and 0 indicates that the corresponding biomarker is invalid, and the L-1 modulus of x and the L-2 modulus of y-Hx are obtained by minimizing Thus, the screening of biomarkers is completed.

[0087] Regarding the device in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0088] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present application scheme. A person of ordinary skill in the art can understand and implement it without paying any creative work.

[0089] Accordingly, the present application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned biomarker screening method based on the differentiable L-1 model. Figure 4 As shown, a hardware structure diagram of a biomarker screening device based on a differentiable L-1 model provided by an embodiment of the present invention is provided in any device with data processing capability, except Figure 4 In addition to the processor, memory and network interface shown, any device with data processing capability in which the apparatus in the embodiment is located may also include other hardware, generally based on the actual functions of the device with data processing capability, which will not be described in detail.

[0090] Accordingly, the present application also provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-mentioned method for screening biomarkers based on a differentiable L-1 model. The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be an external storage device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card (Flash Card), etc. equipped on the device. Further, the computer-readable storage medium may also include both an internal storage unit of any device with data processing capabilities and an external storage device. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or is to be output.

[0091] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the contents disclosed herein. The present application is intended to cover any variations, uses or adaptations of the present application, which follow the general principles of the present application and include common knowledge or customary technical means in the art that are not disclosed in the present application.

[0092] It will be appreciated that the present application is not limited to the exact construction that has been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof.

Claims

1. A method for screening biomarkers based on a differentiable L-1 model, characterized in that: include: (1) Obtaining clinical manifestation data and corresponding biomarkers of the test subjects and performing preprocessing; (2) Based on the clinical performance data and the corresponding biomarkers, the biomarkers are screened by L-1 modulus; wherein the clinical performance data is set as y, the biomarkers are set as matrix H, and the screening of biomarkers is set as vector x, the value of the elements in x is 1 or 0, 1 indicates that the corresponding biomarker is effective, and 0 indicates that the corresponding biomarker is invalid, and the L-1 modulus of x and the L-2 modulus of y-Hx are minimized to obtain Thus, the screening of biomarkers is completed.

2. The method according to claim 1, characterized in that The preprocessing in step (1) includes filling in the missing data by linear or nonlinear interpolation and standardizing the data to transform the data into a Gaussian distribution with a mean of zero and a variance of 1.

3. The method according to claim 1, characterized in that The objective function for biomarker screening is: Where α is the weight coefficient, for L-1 module.

4. The method according to claim 1, characterized in that: The objective function for biomarker screening is: Where α is the weight coefficient, for L-1 module.

5. The method according to claim 4, characterized in that Solving the objective function yields include: (i) Select a step size parameter β and initialize a The superscript 0 indicates that the current iteration is the 0th iteration; (ii) In the first iteration, calculate For the vector n is the number of biomarkers; (iii) Repeat the iterations of step (ii) until is smaller than a predetermined threshold ε.

6. A biomarker screening device based on a differentiable L-1 model, characterized in that: include: A data acquisition module is used to acquire the clinical manifestation data and corresponding biomarkers of the test subject and perform preprocessing; A biomarker screening module is used to screen the biomarkers through the L-1 module according to the clinical performance data and the corresponding biomarkers; wherein the clinical performance data is set as y, the biomarker is set as the matrix H, and the screening of the biomarker is set as the vector x, the value of the element in x is 1 or 0, 1 indicates that the corresponding biomarker is effective, and 0 indicates that the corresponding biomarker is invalid, and the L-1 module of x and the L-2 module of y-Hx are minimized to obtain Thus, the screening of biomarkers is completed.

7. An electronic device, characterized in that: include: one or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the instruction is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

Images